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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |2x + -14| = 2 | |2x + -14| = 2 | 6, 8 | six, eight | 6, 8 | Final answer is: six, eight. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:2:-14:2",
"case_id": "two_solution_integer:2:-14:2",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "6, 8",
"values": [
2,
-14,
2
... | two_solution_integer:2:-14:2 | two_solution_integer | two_solution_integer | two_solution_integer:2:-14:2 | d547144ed84ed68fd9bcfb58c56960e6c1fdc711e5ce0954ae952e61abf7d9cb | two_solution_integer:2:-14:2 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |2x + -9| = -4 | |2x + -9| = -4 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:2:-9:-4",
"case_id": "no_solution_basic:2:-9:-4",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
2,
-9,
-4
],
"f... | no_solution_basic:2:-9:-4 | no_solution_basic | no_solution_basic | no_solution_basic:2:-9:-4 | e4544d13c473a464551d37fbe4d8577026f765cb194befcb8cf89e152a2477f5 | no_solution_basic:2:-9:-4 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |4x + 12| = 12 | |4x + 12| = 12 | -6, 0 | negative six, zero | -6, 0 | Final answer is: negative six, zero. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:4:12:12",
"case_id": "two_solution_integer:4:12:12",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-6, 0",
"values": [
4,
12,
12
... | two_solution_integer:4:12:12 | two_solution_integer | two_solution_integer | two_solution_integer:4:12:12 | 7b5430df149ec0adaf055c73a3634a1301c58c79826911430bc5ce664a5e05ab | two_solution_integer:4:12:12 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |-2x + -12| = 10 | |-2x + -12| = 10 | -11, -1 | negative eleven, negative one | -11, -1 | Final answer is: negative eleven, negative one. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-2:-12:10",
"case_id": "two_solution_integer:-2:-12:10",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-11, -1",
"values": [
-2,
-12,... | two_solution_integer:-2:-12:10 | two_solution_integer | two_solution_integer | two_solution_integer:-2:-12:10 | 23a2f9ceb626f9126a418b3654a0ede145288fe888147212dceb771ac86355af | two_solution_integer:-2:-12:10 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |1x + 11| = -6 | |1x + 11| = -6 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:1:11:-6",
"case_id": "no_solution_basic:1:11:-6",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
1,
11,
-6
],
"f... | no_solution_basic:1:11:-6 | no_solution_basic | no_solution_basic | no_solution_basic:1:11:-6 | fdabf4f5ebd702b6b1b70c3599a42b8c8957aedb84cabb6c0d8f113579ca6133 | no_solution_basic:1:11:-6 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |-4x + 16| = 12 | |-4x + 16| = 12 | 1, 7 | one, seven | 1, 7 | Final answer is: one, seven. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-4:16:12",
"case_id": "two_solution_integer:-4:16:12",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "1, 7",
"values": [
-4,
16,
1... | two_solution_integer:-4:16:12 | two_solution_integer | two_solution_integer | two_solution_integer:-4:16:12 | 84789d0c86ec48a7427c4116606bb0a8dec726f62de991f959118552c83ee6f3 | two_solution_integer:-4:16:12 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |3x + -18| = 9 | |3x + -18| = 9 | 3, 9 | three, nine | 3, 9 | Final answer is: three, nine. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:3:-18:9",
"case_id": "two_solution_integer:3:-18:9",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "3, 9",
"values": [
3,
-18,
9
... | two_solution_integer:3:-18:9 | two_solution_integer | two_solution_integer | two_solution_integer:3:-18:9 | 889ba1328e8bfabefe8d02bc8dfc3857687aba21193178ff807a042a26f69ce2 | two_solution_integer:3:-18:9 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |-2x + -8| = 8 | |-2x + -8| = 8 | -8, 0 | negative eight, zero | -8, 0 | Final answer is: negative eight, zero. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-2:-8:8",
"case_id": "two_solution_integer:-2:-8:8",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-8, 0",
"values": [
-2,
-8,
8
... | two_solution_integer:-2:-8:8 | two_solution_integer | two_solution_integer | two_solution_integer:-2:-8:8 | 053596b975e68786884e507bf6629fe0d0475abdc829d3278948b6957989705c | two_solution_integer:-2:-8:8 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |3x + -4| = -3 | |3x + -4| = -3 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:3:-4:-3",
"case_id": "no_solution_basic:3:-4:-3",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
3,
-4,
-3
],
"f... | no_solution_basic:3:-4:-3 | no_solution_basic | no_solution_basic | no_solution_basic:3:-4:-3 | 0f4d0743897f482127eb66a6cfb083f3f619542fb4c2e159d8674c6cff89b593 | no_solution_basic:3:-4:-3 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |2x + -16| = 10 | |2x + -16| = 10 | 3, 13 | three, thirteen | 3, 13 | Final answer is: three, thirteen. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:2:-16:10",
"case_id": "two_solution_integer:2:-16:10",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "3, 13",
"values": [
2,
-16,
... | two_solution_integer:2:-16:10 | two_solution_integer | two_solution_integer | two_solution_integer:2:-16:10 | 247a2637dba3e98fb6d6a3a748c51ad6b23fcd8dc3cc85c8a9483300b01cb8db | two_solution_integer:2:-16:10 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |-2x + 10| = 2 | |-2x + 10| = 2 | 4, 6 | four, six | 4, 6 | Final answer is: four, six. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-2:10:2",
"case_id": "two_solution_integer:-2:10:2",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "4, 6",
"values": [
-2,
10,
2
... | two_solution_integer:-2:10:2 | two_solution_integer | two_solution_integer | two_solution_integer:-2:10:2 | 90a3b7424e748eae1cd6f5b00a373ac47a175ebca5bb6cf258107a9bf8a1f21f | two_solution_integer:-2:10:2 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |2x + 8| = 10 | |2x + 8| = 10 | -9, 1 | negative nine, one | -9, 1 | Final answer is: negative nine, one. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:2:8:10",
"case_id": "two_solution_integer:2:8:10",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-9, 1",
"values": [
2,
8,
10
]... | two_solution_integer:2:8:10 | two_solution_integer | two_solution_integer | two_solution_integer:2:8:10 | 3842bde344b0815ed2c2be95955f9f74cafd6742f61ee0984620dbfcd6674bee | two_solution_integer:2:8:10 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |3x + -5| = -1 | |3x + -5| = -1 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:3:-5:-1",
"case_id": "no_solution_basic:3:-5:-1",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
3,
-5,
-1
],
"f... | no_solution_basic:3:-5:-1 | no_solution_basic | no_solution_basic | no_solution_basic:3:-5:-1 | a1ec8c8e00dfb883c0ff39c7219a0f4540ab1489d3fec0b078c42b8acebaea0a | no_solution_basic:3:-5:-1 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |-2x + 8| = 10 | |-2x + 8| = 10 | -1, 9 | negative one, nine | -1, 9 | Final answer is: negative one, nine. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-2:8:10",
"case_id": "two_solution_integer:-2:8:10",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-1, 9",
"values": [
-2,
8,
10
... | two_solution_integer:-2:8:10 | two_solution_integer | two_solution_integer | two_solution_integer:-2:8:10 | e278aee965e516b35d5471fad14b87fa07556ef56905e5a8380d789f5afff001 | two_solution_integer:-2:8:10 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |-2x + -18| = 6 | |-2x + -18| = 6 | -12, -6 | negative twelve, negative six | -12, -6 | Final answer is: negative twelve, negative six. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-2:-18:6",
"case_id": "two_solution_integer:-2:-18:6",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-12, -6",
"values": [
-2,
-18,
... | two_solution_integer:-2:-18:6 | two_solution_integer | two_solution_integer | two_solution_integer:-2:-18:6 | 38dd94843bf0c4b49b6494016a55afaf74fe15c76bfbec7e325ea42307f46a96 | two_solution_integer:-2:-18:6 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |-4x + 8| = 4 | |-4x + 8| = 4 | 1, 3 | one, three | 1, 3 | Final answer is: one, three. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-4:8:4",
"case_id": "two_solution_integer:-4:8:4",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "1, 3",
"values": [
-4,
8,
4
],... | two_solution_integer:-4:8:4 | two_solution_integer | two_solution_integer | two_solution_integer:-4:8:4 | 4ed1c1199310d3f9c832d576ecf6722e852df5559e2ad748ef56f829bb5e5b02 | two_solution_integer:-4:8:4 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |3x + -6| = 9 | |3x + -6| = 9 | -1, 5 | negative one, five | -1, 5 | Final answer is: negative one, five. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:3:-6:9",
"case_id": "two_solution_integer:3:-6:9",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-1, 5",
"values": [
3,
-6,
9
]... | two_solution_integer:3:-6:9 | two_solution_integer | two_solution_integer | two_solution_integer:3:-6:9 | 544905d1eb0b5fc15fe43fc8d6906eeb8ad7c9acc28eeac68a60c8e544b24314 | two_solution_integer:3:-6:9 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |1x + -10| = -9 | |1x + -10| = -9 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:1:-10:-9",
"case_id": "no_solution_basic:1:-10:-9",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
1,
-10,
-9
],
... | no_solution_basic:1:-10:-9 | no_solution_basic | no_solution_basic | no_solution_basic:1:-10:-9 | d61a014949927a10f0483817cfb310f1fb9cbf66070af4e859bfd8f33743d6e4 | no_solution_basic:1:-10:-9 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |1x + 10| = -9 | |1x + 10| = -9 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:1:10:-9",
"case_id": "no_solution_basic:1:10:-9",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
1,
10,
-9
],
"f... | no_solution_basic:1:10:-9 | no_solution_basic | no_solution_basic | no_solution_basic:1:10:-9 | 02f075475b6bb65822fe03e4e85281505504391a08ff2238ea5798bc3c7f02ec | no_solution_basic:1:10:-9 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |1x + -9| = -1 | |1x + -9| = -1 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:1:-9:-1",
"case_id": "no_solution_basic:1:-9:-1",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
1,
-9,
-1
],
"f... | no_solution_basic:1:-9:-1 | no_solution_basic | no_solution_basic | no_solution_basic:1:-9:-1 | 3fd230d4acfc2a6b104fd54585fa6887e0aa0afd637d923e14a030011dcc817a | no_solution_basic:1:-9:-1 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |-4x + 10| = 14 | |-4x + 10| = 14 | -1, 6 | negative one, six | -1, 6 | Final answer is: negative one, six. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-4:10:14",
"case_id": "two_solution_integer:-4:10:14",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-1, 6",
"values": [
-4,
10,
... | two_solution_integer:-4:10:14 | two_solution_integer | two_solution_integer | two_solution_integer:-4:10:14 | 7f9c022c5f41e8f40eb224d4c18fd7de511ab1856912dded121ca83bb36a3f1f | two_solution_integer:-4:10:14 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |3x + -9| = -3 | |3x + -9| = -3 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:3:-9:-3",
"case_id": "no_solution_basic:3:-9:-3",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
3,
-9,
-3
],
"f... | no_solution_basic:3:-9:-3 | no_solution_basic | no_solution_basic | no_solution_basic:3:-9:-3 | 7d885ae6c146ab6972573d6606ab7f2471c305a9d25749c1f8e2bc5a68c9152f | no_solution_basic:3:-9:-3 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |2x + -3| = -4 | |2x + -3| = -4 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:2:-3:-4",
"case_id": "no_solution_basic:2:-3:-4",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
2,
-3,
-4
],
"f... | no_solution_basic:2:-3:-4 | no_solution_basic | no_solution_basic | no_solution_basic:2:-3:-4 | 1d6c87090ef20d100028886c34a4f36a03e61f7aa5cc44a849d8beffdd1c2896 | no_solution_basic:2:-3:-4 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |1x + -5| = -9 | |1x + -5| = -9 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:1:-5:-9",
"case_id": "no_solution_basic:1:-5:-9",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
1,
-5,
-9
],
"f... | no_solution_basic:1:-5:-9 | no_solution_basic | no_solution_basic | no_solution_basic:1:-5:-9 | 945321c9b2f3978b621df5e920b2abfb0c8c50ed0a8b834792e546aac7eee68b | no_solution_basic:1:-5:-9 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |4x + 18| = 14 | |4x + 18| = 14 | -8, -1 | negative eight, negative one | -8, -1 | Final answer is: negative eight, negative one. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:4:18:14",
"case_id": "two_solution_integer:4:18:14",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-8, -1",
"values": [
4,
18,
14... | two_solution_integer:4:18:14 | two_solution_integer | two_solution_integer | two_solution_integer:4:18:14 | e63c58dbb95098d0dc3d8474a0c11850f18009ff2cac33c71ebd00085c443d96 | two_solution_integer:4:18:14 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |1x + -5| = -6 | |1x + -5| = -6 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:1:-5:-6",
"case_id": "no_solution_basic:1:-5:-6",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
1,
-5,
-6
],
"f... | no_solution_basic:1:-5:-6 | no_solution_basic | no_solution_basic | no_solution_basic:1:-5:-6 | 842514b565aa4f8a40a854ea6622f7efd05972a05667e698028bd88d0dd05c25 | no_solution_basic:1:-5:-6 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |-2x + -10| = 4 | |-2x + -10| = 4 | -7, -3 | negative seven, negative three | -7, -3 | Final answer is: negative seven, negative three. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-2:-10:4",
"case_id": "two_solution_integer:-2:-10:4",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-7, -3",
"values": [
-2,
-10,
... | two_solution_integer:-2:-10:4 | two_solution_integer | two_solution_integer | two_solution_integer:-2:-10:4 | 92bf9564f52d8ec5ca5fa13237f3daed2c014ae252f1d9fc440ae765a17be100 | two_solution_integer:-2:-10:4 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |2x + 8| = -6 | |2x + 8| = -6 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:2:8:-6",
"case_id": "no_solution_basic:2:8:-6",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
2,
8,
-6
],
"fina... | no_solution_basic:2:8:-6 | no_solution_basic | no_solution_basic | no_solution_basic:2:8:-6 | d887f91187e5f7d83e7304b0fb8b3f65f2d9042d114968850022e0d38fe29a05 | no_solution_basic:2:8:-6 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |-2x + 12| = 4 | |-2x + 12| = 4 | 4, 8 | four, eight | 4, 8 | Final answer is: four, eight. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-2:12:4",
"case_id": "two_solution_integer:-2:12:4",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "4, 8",
"values": [
-2,
12,
4
... | two_solution_integer:-2:12:4 | two_solution_integer | two_solution_integer | two_solution_integer:-2:12:4 | 170f13d744c223409b6742706d97938721078360ab9007d85482d6dc3763e5e3 | two_solution_integer:-2:12:4 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |1x + -5| = -3 | |1x + -5| = -3 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:1:-5:-3",
"case_id": "no_solution_basic:1:-5:-3",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
1,
-5,
-3
],
"f... | no_solution_basic:1:-5:-3 | no_solution_basic | no_solution_basic | no_solution_basic:1:-5:-3 | c588ae22022df3f372ff7ba0e709ec976e52bd7227bb6c5285580cad5ef45318 | no_solution_basic:1:-5:-3 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |2x + 11| = -7 | |2x + 11| = -7 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:2:11:-7",
"case_id": "no_solution_basic:2:11:-7",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
2,
11,
-7
],
"f... | no_solution_basic:2:11:-7 | no_solution_basic | no_solution_basic | no_solution_basic:2:11:-7 | 731c0d48e1c55967e5922c509bb4a1ad3b62f5d783a5079297171e56390d7bd3 | no_solution_basic:2:11:-7 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |-4x + 2| = 10 | |-4x + 2| = 10 | -2, 3 | negative two, three | -2, 3 | Final answer is: negative two, three. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-4:2:10",
"case_id": "two_solution_integer:-4:2:10",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-2, 3",
"values": [
-4,
2,
10
... | two_solution_integer:-4:2:10 | two_solution_integer | two_solution_integer | two_solution_integer:-4:2:10 | 6a726dd08e4c26570bc1331ab381cd6358d68a9c8f21af687195024511c5394d | two_solution_integer:-4:2:10 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |2x + -1| = -8 | |2x + -1| = -8 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:2:-1:-8",
"case_id": "no_solution_basic:2:-1:-8",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
2,
-1,
-8
],
"f... | no_solution_basic:2:-1:-8 | no_solution_basic | no_solution_basic | no_solution_basic:2:-1:-8 | f745493a2e63b5771ba5ab07510b42baadb0135e5f644a25a309bd3a3c84686b | no_solution_basic:2:-1:-8 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |1x + -4| = -5 | |1x + -4| = -5 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:1:-4:-5",
"case_id": "no_solution_basic:1:-4:-5",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
1,
-4,
-5
],
"f... | no_solution_basic:1:-4:-5 | no_solution_basic | no_solution_basic | no_solution_basic:1:-4:-5 | f253c64a6517e0ab1dec952ba2dcd90ef31a6a85b10b5ec66b8a304aada5992c | no_solution_basic:1:-4:-5 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |-4x + 14| = 14 | |-4x + 14| = 14 | 0, 7 | zero, seven | 0, 7 | Final answer is: zero, seven. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-4:14:14",
"case_id": "two_solution_integer:-4:14:14",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "0, 7",
"values": [
-4,
14,
1... | two_solution_integer:-4:14:14 | two_solution_integer | two_solution_integer | two_solution_integer:-4:14:14 | 7a0fee7577cb7fa153e7b0aba7df7648b9a2123c3516d486547bf0454e7b576f | two_solution_integer:-4:14:14 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |1x + 7| = -10 | |1x + 7| = -10 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:1:7:-10",
"case_id": "no_solution_basic:1:7:-10",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
1,
7,
-10
],
"f... | no_solution_basic:1:7:-10 | no_solution_basic | no_solution_basic | no_solution_basic:1:7:-10 | 113f262c705d9fd679cda09363519e4b1c8ed0913246878c240baf21ed9908e2 | no_solution_basic:1:7:-10 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |-4x + -2| = 6 | |-4x + -2| = 6 | -2, 1 | negative two, one | -2, 1 | Final answer is: negative two, one. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-4:-2:6",
"case_id": "two_solution_integer:-4:-2:6",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-2, 1",
"values": [
-4,
-2,
6
... | two_solution_integer:-4:-2:6 | two_solution_integer | two_solution_integer | two_solution_integer:-4:-2:6 | dd80dd03840be241a58b3a078784b355baae343d630dc85cd29a75605575cd32 | two_solution_integer:-4:-2:6 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |2x + 4| = 8 | |2x + 4| = 8 | -6, 2 | negative six, two | -6, 2 | Final answer is: negative six, two. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:2:4:8",
"case_id": "two_solution_integer:2:4:8",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-6, 2",
"values": [
2,
4,
8
],
... | two_solution_integer:2:4:8 | two_solution_integer | two_solution_integer | two_solution_integer:2:4:8 | 571003051976614e265776cef3b50b11bddb8b49837e79f167fcdff024c091b4 | two_solution_integer:2:4:8 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |-4x + -14| = 10 | |-4x + -14| = 10 | -6, -1 | negative six, negative one | -6, -1 | Final answer is: negative six, negative one. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-4:-14:10",
"case_id": "two_solution_integer:-4:-14:10",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-6, -1",
"values": [
-4,
-14,
... | two_solution_integer:-4:-14:10 | two_solution_integer | two_solution_integer | two_solution_integer:-4:-14:10 | a7ced84217c9364606a112fa4ad8111893d6ee452ad0492c5673431f44238ae0 | two_solution_integer:-4:-14:10 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |1x + 12| = -9 | |1x + 12| = -9 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:1:12:-9",
"case_id": "no_solution_basic:1:12:-9",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
1,
12,
-9
],
"f... | no_solution_basic:1:12:-9 | no_solution_basic | no_solution_basic | no_solution_basic:1:12:-9 | 3d06d9b7804f79c67b1ea392c37ead41c8c7b4a0c2f461605097c9e83d0c6a01 | no_solution_basic:1:12:-9 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |1x + -1| = -6 | |1x + -1| = -6 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:1:-1:-6",
"case_id": "no_solution_basic:1:-1:-6",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
1,
-1,
-6
],
"f... | no_solution_basic:1:-1:-6 | no_solution_basic | no_solution_basic | no_solution_basic:1:-1:-6 | 5849b542bc40d9750332f02bcab1ac5a1e639dc77c02e3741d65b34683a24a90 | no_solution_basic:1:-1:-6 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |2x + -10| = -3 | |2x + -10| = -3 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:2:-10:-3",
"case_id": "no_solution_basic:2:-10:-3",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
2,
-10,
-3
],
... | no_solution_basic:2:-10:-3 | no_solution_basic | no_solution_basic | no_solution_basic:2:-10:-3 | 4c96f11ecef669a5e8649f3bed8ea8496d7e3c46f0e88dbce517f571fb272ccf | no_solution_basic:2:-10:-3 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |-4x + -14| = 2 | |-4x + -14| = 2 | -4, -3 | negative four, negative three | -4, -3 | Final answer is: negative four, negative three. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-4:-14:2",
"case_id": "two_solution_integer:-4:-14:2",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-4, -3",
"values": [
-4,
-14,
... | two_solution_integer:-4:-14:2 | two_solution_integer | two_solution_integer | two_solution_integer:-4:-14:2 | 5cad294f74c555990af07cd7f055b2a5bc606dd1111fa16bf41f8bce142bdbf3 | two_solution_integer:-4:-14:2 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |3x + -10| = -8 | |3x + -10| = -8 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:3:-10:-8",
"case_id": "no_solution_basic:3:-10:-8",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
3,
-10,
-8
],
... | no_solution_basic:3:-10:-8 | no_solution_basic | no_solution_basic | no_solution_basic:3:-10:-8 | 70be6dc2afd115a3ea481d093c62d5ba89468bb733a5da31a9e1e17c1b2d9607 | no_solution_basic:3:-10:-8 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |2x + 1| = -5 | |2x + 1| = -5 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:2:1:-5",
"case_id": "no_solution_basic:2:1:-5",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
2,
1,
-5
],
"fina... | no_solution_basic:2:1:-5 | no_solution_basic | no_solution_basic | no_solution_basic:2:1:-5 | b470337c11813787f0d81f39326b3f966218add44447ca7f7d55ab82f29967df | no_solution_basic:2:1:-5 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |-4x + -4| = 12 | |-4x + -4| = 12 | -4, 2 | negative four, two | -4, 2 | Final answer is: negative four, two. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-4:-4:12",
"case_id": "two_solution_integer:-4:-4:12",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-4, 2",
"values": [
-4,
-4,
... | two_solution_integer:-4:-4:12 | two_solution_integer | two_solution_integer | two_solution_integer:-4:-4:12 | 269c446431244b1e0423fce4b55248fc388ce1bc0a9c0cb6a33fa457be381ba5 | two_solution_integer:-4:-4:12 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |2x + 3| = -3 | |2x + 3| = -3 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:2:3:-3",
"case_id": "no_solution_basic:2:3:-3",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
2,
3,
-3
],
"fina... | no_solution_basic:2:3:-3 | no_solution_basic | no_solution_basic | no_solution_basic:2:3:-3 | 29c82e06d179a3665232a6f90c9e099e840096c89777e4075f1e3f5be06a5b21 | no_solution_basic:2:3:-3 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |2x + 5| = -8 | |2x + 5| = -8 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:2:5:-8",
"case_id": "no_solution_basic:2:5:-8",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
2,
5,
-8
],
"fina... | no_solution_basic:2:5:-8 | no_solution_basic | no_solution_basic | no_solution_basic:2:5:-8 | f1faaf448773d4485f639ac80a4ab2d38c18960fd29d2776860e05edfd988de6 | no_solution_basic:2:5:-8 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |2x + 1| = -9 | |2x + 1| = -9 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:2:1:-9",
"case_id": "no_solution_basic:2:1:-9",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
2,
1,
-9
],
"fina... | no_solution_basic:2:1:-9 | no_solution_basic | no_solution_basic | no_solution_basic:2:1:-9 | fb7c085e11939840b3d739c6b87f73c950fb4f2c679bf40c239da227d03b3880 | no_solution_basic:2:1:-9 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |1x + -12| = -5 | |1x + -12| = -5 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:1:-12:-5",
"case_id": "no_solution_basic:1:-12:-5",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
1,
-12,
-5
],
... | no_solution_basic:1:-12:-5 | no_solution_basic | no_solution_basic | no_solution_basic:1:-12:-5 | 645bdb538c008840740c44c93043ded189158b30fddd5ea4dd4b5d1bcefce7c6 | no_solution_basic:1:-12:-5 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |2x + -2| = -10 | |2x + -2| = -10 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:2:-2:-10",
"case_id": "no_solution_basic:2:-2:-10",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
2,
-2,
-10
],
... | no_solution_basic:2:-2:-10 | no_solution_basic | no_solution_basic | no_solution_basic:2:-2:-10 | 7d9a22c841e7b03465656cc89a4b9f94e57e0cb59b35e90b495e287078da5d45 | no_solution_basic:2:-2:-10 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve the absolute value equation: |2x + -1| = -3 | |2x + -1| = -3 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:2:-1:-3",
"case_id": "no_solution_basic:2:-1:-3",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
2,
-1,
-3
],
"f... | no_solution_basic:2:-1:-3 | no_solution_basic | no_solution_basic | no_solution_basic:2:-1:-3 | 690e53599d72263de13148b2ec9005ef280c34b1b2920d4c2ac93c9ab6978a4d | no_solution_basic:2:-1:-3 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Find all real solutions: |-2x + 6| = 10 | |-2x + 6| = 10 | -2, 8 | negative two, eight | -2, 8 | Final answer is: negative two, eight. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-2:6:10",
"case_id": "two_solution_integer:-2:6:10",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-2, 8",
"values": [
-2,
6,
10
... | two_solution_integer:-2:6:10 | two_solution_integer | two_solution_integer | two_solution_integer:-2:6:10 | ccdabef4cc8876ad36ced201c33dd6aa4d81314133e618c33c6489d32cdf05ad | two_solution_integer:-2:6:10 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Work through the absolute value cases: |-2x + -2| = 6 | |-2x + -2| = 6 | -4, 2 | negative four, two | -4, 2 | Final answer is: negative four, two. | {
"family": "two_solution_integer",
"level_number": 3,
"structured": true,
"canonical_key": "two_solution_integer:-2:-2:6",
"case_id": "two_solution_integer:-2:-2:6",
"family_id": "two_solution_integer",
"template_id": "two_solution_integer",
"final_answer": "-4, 2",
"values": [
-2,
-2,
6
... | two_solution_integer:-2:-2:6 | two_solution_integer | two_solution_integer | two_solution_integer:-2:-2:6 | a79e4c7bd1711a40ff7e9fea7a04bd6e28188da2dbb3af50085d3210e7385e46 | two_solution_integer:-2:-2:6 |
algebra.absolute_value_equations | algebra | core_algebra | level_3 | level_3 | Solve for x: |3x + -7| = -8 | |3x + -7| = -8 | no solution | no solution | no solution | Final answer is: no solution. | {
"family": "no_solution_basic",
"level_number": 3,
"structured": true,
"canonical_key": "no_solution_basic:3:-7:-8",
"case_id": "no_solution_basic:3:-7:-8",
"family_id": "no_solution_basic",
"template_id": "no_solution_basic",
"final_answer": "no solution",
"values": [
3,
-7,
-8
],
"f... | no_solution_basic:3:-7:-8 | no_solution_basic | no_solution_basic | no_solution_basic:3:-7:-8 | ceee628f1a6cc148f0f57764f3ed120e49a0a8d2023aaa8d272976e6ef71ab8c | no_solution_basic:3:-7:-8 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve the absolute value equation: |x - (14)| = 3 | |x - (14)| = 3 | 11, 17 | eleven, seventeen | 11, 17 | Final answer is: eleven, seventeen. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:14:3",
"case_id": "x_minus_h_eq_k:14:3",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "11, 17",
"values": [
14,
3
],
"final_answer_words": "Final answer ... | x_minus_h_eq_k:14:3 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:14:3 | 7a16356be07fb1085bcb87b59576781a58b7302e65be552d78343ffee2b9b019 | x_minus_h_eq_k:14:3 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Find all real solutions: |x - (4)| = 7 | |x - (4)| = 7 | -3, 11 | negative three, eleven | -3, 11 | Final answer is: negative three, eleven. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:4:7",
"case_id": "x_minus_h_eq_k:4:7",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-3, 11",
"values": [
4,
7
],
"final_answer_words": "Final answer is:... | x_minus_h_eq_k:4:7 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:4:7 | 046c7bd1c6fa58f52aa5fcd130608f2393f4f6e199a2c8e5239882f0d59b4b76 | x_minus_h_eq_k:4:7 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Work through the absolute value cases: |x - (-11)| = 2 | |x - (-11)| = 2 | -13, -9 | negative thirteen, negative nine | -13, -9 | Final answer is: negative thirteen, negative nine. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-11:2",
"case_id": "x_minus_h_eq_k:-11:2",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-13, -9",
"values": [
-11,
2
],
"final_answer_words": "Final ans... | x_minus_h_eq_k:-11:2 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-11:2 | 7751eaf582360a65469d9515408794712ff90295493ced29b326860e1b931763 | x_minus_h_eq_k:-11:2 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve the absolute value equation: |x - (-7)| = 7 | |x - (-7)| = 7 | -14, 0 | negative fourteen, zero | -14, 0 | Final answer is: negative fourteen, zero. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-7:7",
"case_id": "x_minus_h_eq_k:-7:7",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-14, 0",
"values": [
-7,
7
],
"final_answer_words": "Final answer ... | x_minus_h_eq_k:-7:7 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-7:7 | 56a5ad816d13647bc3fd5545e051cd5be1f74fa06f62d2b7be9868495c41a764 | x_minus_h_eq_k:-7:7 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Find all real solutions: |x - (-20)| = 1 | |x - (-20)| = 1 | -21, -19 | negative twenty-one, negative nineteen | -21, -19 | Final answer is: negative twenty-one, negative nineteen. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-20:1",
"case_id": "x_minus_h_eq_k:-20:1",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-21, -19",
"values": [
-20,
1
],
"final_answer_words": "Final an... | x_minus_h_eq_k:-20:1 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-20:1 | a096230fe4dfecafd101cd52046dd879261776adad470e3c797b4db93ef8a6e8 | x_minus_h_eq_k:-20:1 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Work through the absolute value cases: |x - (9)| = 13 | |x - (9)| = 13 | -4, 22 | negative four, twenty-two | -4, 22 | Final answer is: negative four, twenty-two. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:9:13",
"case_id": "x_minus_h_eq_k:9:13",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-4, 22",
"values": [
9,
13
],
"final_answer_words": "Final answer ... | x_minus_h_eq_k:9:13 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:9:13 | f8d588924ebdf5188775baee83f46f20c198b210b4f45a0f429a63994aea4990 | x_minus_h_eq_k:9:13 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve for x: |x - (2)| = 15 | |x - (2)| = 15 | -13, 17 | negative thirteen, seventeen | -13, 17 | Final answer is: negative thirteen, seventeen. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:2:15",
"case_id": "x_minus_h_eq_k:2:15",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-13, 17",
"values": [
2,
15
],
"final_answer_words": "Final answer... | x_minus_h_eq_k:2:15 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:2:15 | 9f062df2d01a097b3e19dedffcf7c3e1c2de66815cdb06f214e2607b7d1407c5 | x_minus_h_eq_k:2:15 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve the absolute value equation: |x - (-9)| = 6 | |x - (-9)| = 6 | -15, -3 | negative fifteen, negative three | -15, -3 | Final answer is: negative fifteen, negative three. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-9:6",
"case_id": "x_minus_h_eq_k:-9:6",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-15, -3",
"values": [
-9,
6
],
"final_answer_words": "Final answer... | x_minus_h_eq_k:-9:6 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-9:6 | 4c4ece58e02cec1700fb6749947d4be9cd7997f9dd3015f62780b29491577bb6 | x_minus_h_eq_k:-9:6 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Find all real solutions: |x - (-14)| = 5 | |x - (-14)| = 5 | -19, -9 | negative nineteen, negative nine | -19, -9 | Final answer is: negative nineteen, negative nine. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-14:5",
"case_id": "x_minus_h_eq_k:-14:5",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-19, -9",
"values": [
-14,
5
],
"final_answer_words": "Final ans... | x_minus_h_eq_k:-14:5 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-14:5 | b3e0bfddb0b8eb76cfd137e11972202bdd344907b9cfdaf4ddcf6a723da211fa | x_minus_h_eq_k:-14:5 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Work through the absolute value cases: |x - (4)| = 9 | |x - (4)| = 9 | -5, 13 | negative five, thirteen | -5, 13 | Final answer is: negative five, thirteen. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:4:9",
"case_id": "x_minus_h_eq_k:4:9",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-5, 13",
"values": [
4,
9
],
"final_answer_words": "Final answer is:... | x_minus_h_eq_k:4:9 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:4:9 | 298e6751de5d00d55bb931a65f5e4d1ff372e5359c67e933a60d42d40b2093d9 | x_minus_h_eq_k:4:9 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve for x: |x - (20)| = 14 | |x - (20)| = 14 | 6, 34 | six, thirty-four | 6, 34 | Final answer is: six, thirty-four. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:20:14",
"case_id": "x_minus_h_eq_k:20:14",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "6, 34",
"values": [
20,
14
],
"final_answer_words": "Final answe... | x_minus_h_eq_k:20:14 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:20:14 | fd2466e3f5ee0f0a96b7013b2bb964e31d675d36c323c4a5ab6b5effbcdfbf83 | x_minus_h_eq_k:20:14 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve the absolute value equation: |x - (11)| = 5 | |x - (11)| = 5 | 6, 16 | six, sixteen | 6, 16 | Final answer is: six, sixteen. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:11:5",
"case_id": "x_minus_h_eq_k:11:5",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "6, 16",
"values": [
11,
5
],
"final_answer_words": "Final answer i... | x_minus_h_eq_k:11:5 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:11:5 | aec83cd977599c0e59a2e1c02057ca6dbefb2a6717cd5a65b777cdc5de76d55d | x_minus_h_eq_k:11:5 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Find all real solutions: |x - (-3)| = 5 | |x - (-3)| = 5 | -8, 2 | negative eight, two | -8, 2 | Final answer is: negative eight, two. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-3:5",
"case_id": "x_minus_h_eq_k:-3:5",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-8, 2",
"values": [
-3,
5
],
"final_answer_words": "Final answer i... | x_minus_h_eq_k:-3:5 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-3:5 | b2046692a72c13510f6e20d4f2fe3c1236b1c91030b1b9753fe5fa33142dbe15 | x_minus_h_eq_k:-3:5 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Work through the absolute value cases: |x - (5)| = 8 | |x - (5)| = 8 | -3, 13 | negative three, thirteen | -3, 13 | Final answer is: negative three, thirteen. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:5:8",
"case_id": "x_minus_h_eq_k:5:8",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-3, 13",
"values": [
5,
8
],
"final_answer_words": "Final answer is:... | x_minus_h_eq_k:5:8 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:5:8 | 8eef301bd0068f37fa48b0f48308acffa3aa44e4e192a497de005668fa8035da | x_minus_h_eq_k:5:8 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve for x: |x - (-8)| = 7 | |x - (-8)| = 7 | -15, -1 | negative fifteen, negative one | -15, -1 | Final answer is: negative fifteen, negative one. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-8:7",
"case_id": "x_minus_h_eq_k:-8:7",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-15, -1",
"values": [
-8,
7
],
"final_answer_words": "Final answer... | x_minus_h_eq_k:-8:7 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-8:7 | 37ac69b8df87244777de9a3a83d2331167faf54240139a5ff512b8ff7cd6d321 | x_minus_h_eq_k:-8:7 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve the absolute value equation: |x - (-5)| = 9 | |x - (-5)| = 9 | -14, 4 | negative fourteen, four | -14, 4 | Final answer is: negative fourteen, four. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-5:9",
"case_id": "x_minus_h_eq_k:-5:9",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-14, 4",
"values": [
-5,
9
],
"final_answer_words": "Final answer ... | x_minus_h_eq_k:-5:9 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-5:9 | c7ffc09d8ecbdc61922e468617d25a8e92f3e40fdf55f4a91763c47847fbf3af | x_minus_h_eq_k:-5:9 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Find all real solutions: |x - (-15)| = 15 | |x - (-15)| = 15 | -30, 0 | negative thirty, zero | -30, 0 | Final answer is: negative thirty, zero. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-15:15",
"case_id": "x_minus_h_eq_k:-15:15",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-30, 0",
"values": [
-15,
15
],
"final_answer_words": "Final a... | x_minus_h_eq_k:-15:15 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-15:15 | 6ecac0664b22d34ed91dbd640f1ed60ce1a1d6a8544101163e44fbe86b0cec78 | x_minus_h_eq_k:-15:15 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Work through the absolute value cases: |x - (14)| = 1 | |x - (14)| = 1 | 13, 15 | thirteen, fifteen | 13, 15 | Final answer is: thirteen, fifteen. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:14:1",
"case_id": "x_minus_h_eq_k:14:1",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "13, 15",
"values": [
14,
1
],
"final_answer_words": "Final answer ... | x_minus_h_eq_k:14:1 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:14:1 | f211656c7ac443d6895a31c09e8d4a7765e4b2649c4d1c69c1b24977fae1027b | x_minus_h_eq_k:14:1 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve for x: |x - (-16)| = 15 | |x - (-16)| = 15 | -31, -1 | negative thirty-one, negative one | -31, -1 | Final answer is: negative thirty-one, negative one. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-16:15",
"case_id": "x_minus_h_eq_k:-16:15",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-31, -1",
"values": [
-16,
15
],
"final_answer_words": "Final ... | x_minus_h_eq_k:-16:15 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-16:15 | 7d96c9b9a5c530d7499409e654b507f72145fe624cd09ae32fa1aea3f9a467ca | x_minus_h_eq_k:-16:15 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve the absolute value equation: |x - (2)| = 11 | |x - (2)| = 11 | -9, 13 | negative nine, thirteen | -9, 13 | Final answer is: negative nine, thirteen. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:2:11",
"case_id": "x_minus_h_eq_k:2:11",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-9, 13",
"values": [
2,
11
],
"final_answer_words": "Final answer ... | x_minus_h_eq_k:2:11 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:2:11 | 6b2e4271ef20084026ea59c9ca0e662c5ea4011c7172f765f0d9860a0d66093e | x_minus_h_eq_k:2:11 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Find all real solutions: |x - (14)| = 11 | |x - (14)| = 11 | 3, 25 | three, twenty-five | 3, 25 | Final answer is: three, twenty-five. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:14:11",
"case_id": "x_minus_h_eq_k:14:11",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "3, 25",
"values": [
14,
11
],
"final_answer_words": "Final answe... | x_minus_h_eq_k:14:11 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:14:11 | e56af8c15418d1dcabdedbaf45a9e41ef57fa0fadc23e291e4abf8b5935173aa | x_minus_h_eq_k:14:11 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Work through the absolute value cases: |x - (2)| = 7 | |x - (2)| = 7 | -5, 9 | negative five, nine | -5, 9 | Final answer is: negative five, nine. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:2:7",
"case_id": "x_minus_h_eq_k:2:7",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-5, 9",
"values": [
2,
7
],
"final_answer_words": "Final answer is: ... | x_minus_h_eq_k:2:7 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:2:7 | d2a1c4e5b6096828ada81242e59644bf0759972c9ea8119bae9fabe7bc9453ad | x_minus_h_eq_k:2:7 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve for x: |x - (11)| = 13 | |x - (11)| = 13 | -2, 24 | negative two, twenty-four | -2, 24 | Final answer is: negative two, twenty-four. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:11:13",
"case_id": "x_minus_h_eq_k:11:13",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-2, 24",
"values": [
11,
13
],
"final_answer_words": "Final answ... | x_minus_h_eq_k:11:13 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:11:13 | 37ca5be6ef2e9672ecd3d2316684e068e06f40fc25900e02705317fedda64f6b | x_minus_h_eq_k:11:13 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Work through the absolute value cases: |x - (0)| = 2 | |x - (0)| = 2 | -2, 2 | negative two, two | -2, 2 | Final answer is: negative two, two. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:0:2",
"case_id": "x_minus_h_eq_k:0:2",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-2, 2",
"values": [
0,
2
],
"final_answer_words": "Final answer is: ... | x_minus_h_eq_k:0:2 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:0:2 | d80f59f7aa627049fba7bb8748154b1826c71ca80c44536f703c79ca53d88767 | x_minus_h_eq_k:0:2 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve for x: |x - (8)| = 15 | |x - (8)| = 15 | -7, 23 | negative seven, twenty-three | -7, 23 | Final answer is: negative seven, twenty-three. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:8:15",
"case_id": "x_minus_h_eq_k:8:15",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-7, 23",
"values": [
8,
15
],
"final_answer_words": "Final answer ... | x_minus_h_eq_k:8:15 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:8:15 | f8864bb4361e9d4b37b43f1c58a7b0bd1f0ab443c1cd996b03b9f3e31d30e13f | x_minus_h_eq_k:8:15 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve the absolute value equation: |x - (20)| = 4 | |x - (20)| = 4 | 16, 24 | sixteen, twenty-four | 16, 24 | Final answer is: sixteen, twenty-four. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:20:4",
"case_id": "x_minus_h_eq_k:20:4",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "16, 24",
"values": [
20,
4
],
"final_answer_words": "Final answer ... | x_minus_h_eq_k:20:4 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:20:4 | 849e7bed58296fd3cf71cec972bb2a2f177e486deca242e96a8c4cea943f84d3 | x_minus_h_eq_k:20:4 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Find all real solutions: |x - (16)| = 15 | |x - (16)| = 15 | 1, 31 | one, thirty-one | 1, 31 | Final answer is: one, thirty-one. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:16:15",
"case_id": "x_minus_h_eq_k:16:15",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "1, 31",
"values": [
16,
15
],
"final_answer_words": "Final answe... | x_minus_h_eq_k:16:15 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:16:15 | c48cdf7440d7b5b0f338c815072b6b4e6dd055d9672c431ebcbf0ebd6bcfb3c9 | x_minus_h_eq_k:16:15 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve for x: |x - (7)| = 6 | |x - (7)| = 6 | 1, 13 | one, thirteen | 1, 13 | Final answer is: one, thirteen. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:7:6",
"case_id": "x_minus_h_eq_k:7:6",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "1, 13",
"values": [
7,
6
],
"final_answer_words": "Final answer is: ... | x_minus_h_eq_k:7:6 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:7:6 | 65cfba66b1a94b5f34c901cff0828fd349c25502c028e96fc90b4cdf1f414c6e | x_minus_h_eq_k:7:6 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve the absolute value equation: |x - (-20)| = 2 | |x - (-20)| = 2 | -22, -18 | negative twenty-two, negative eighteen | -22, -18 | Final answer is: negative twenty-two, negative eighteen. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-20:2",
"case_id": "x_minus_h_eq_k:-20:2",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-22, -18",
"values": [
-20,
2
],
"final_answer_words": "Final an... | x_minus_h_eq_k:-20:2 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-20:2 | bbe60259a2a98992a83db7f67a79942dd3144ece2ef44132468de9ecd92ed670 | x_minus_h_eq_k:-20:2 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Find all real solutions: |x - (-7)| = 15 | |x - (-7)| = 15 | -22, 8 | negative twenty-two, eight | -22, 8 | Final answer is: negative twenty-two, eight. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-7:15",
"case_id": "x_minus_h_eq_k:-7:15",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-22, 8",
"values": [
-7,
15
],
"final_answer_words": "Final answ... | x_minus_h_eq_k:-7:15 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-7:15 | 917b671dec4e6d8366632f6ba5100cb6a0143e561bf9db219879799fc762d4f5 | x_minus_h_eq_k:-7:15 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Work through the absolute value cases: |x - (5)| = 0 | |x - (5)| = 0 | 5 | five | 5 | Final answer is: five. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:5:0",
"case_id": "x_minus_h_eq_k:5:0",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "5",
"values": [
5,
0
],
"final_answer_words": "Final answer is: five... | x_minus_h_eq_k:5:0 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:5:0 | 3eee715c1ff13daff0e76f3a3cb741061b3b1a42b9e5a7fb6c94e9be73044ed4 | x_minus_h_eq_k:5:0 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve for x: |x - (-6)| = 10 | |x - (-6)| = 10 | -16, 4 | negative sixteen, four | -16, 4 | Final answer is: negative sixteen, four. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-6:10",
"case_id": "x_minus_h_eq_k:-6:10",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-16, 4",
"values": [
-6,
10
],
"final_answer_words": "Final answ... | x_minus_h_eq_k:-6:10 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-6:10 | b914099ea724af86892b09baa7fc9d09efc7224db1b57b53a70ca3d70d4a3169 | x_minus_h_eq_k:-6:10 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Find all real solutions: |x - (-11)| = 8 | |x - (-11)| = 8 | -19, -3 | negative nineteen, negative three | -19, -3 | Final answer is: negative nineteen, negative three. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-11:8",
"case_id": "x_minus_h_eq_k:-11:8",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-19, -3",
"values": [
-11,
8
],
"final_answer_words": "Final ans... | x_minus_h_eq_k:-11:8 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-11:8 | 3d79ad6e67e9a231c7d61cba321396c441cc710f2addd6b6fecdcf89fad92f49 | x_minus_h_eq_k:-11:8 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Work through the absolute value cases: |x - (17)| = 6 | |x - (17)| = 6 | 11, 23 | eleven, twenty-three | 11, 23 | Final answer is: eleven, twenty-three. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:17:6",
"case_id": "x_minus_h_eq_k:17:6",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "11, 23",
"values": [
17,
6
],
"final_answer_words": "Final answer ... | x_minus_h_eq_k:17:6 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:17:6 | d62d1a184115ff028a0b3bc697a3ecd5c10a57d7de4a7c4e93c29cd20c021cff | x_minus_h_eq_k:17:6 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve for x: |x - (1)| = 8 | |x - (1)| = 8 | -7, 9 | negative seven, nine | -7, 9 | Final answer is: negative seven, nine. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:1:8",
"case_id": "x_minus_h_eq_k:1:8",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-7, 9",
"values": [
1,
8
],
"final_answer_words": "Final answer is: ... | x_minus_h_eq_k:1:8 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:1:8 | f75611a8848d1f8d31e6e15904c7d9a007c3f3e2c1bb9feae640f59afcadb1e5 | x_minus_h_eq_k:1:8 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve the absolute value equation: |x - (15)| = 7 | |x - (15)| = 7 | 8, 22 | eight, twenty-two | 8, 22 | Final answer is: eight, twenty-two. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:15:7",
"case_id": "x_minus_h_eq_k:15:7",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "8, 22",
"values": [
15,
7
],
"final_answer_words": "Final answer i... | x_minus_h_eq_k:15:7 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:15:7 | 63a693028d9d5915c7bf0ed38acf03b1c86bf3eef16b24b2d6d38bb9147962b5 | x_minus_h_eq_k:15:7 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Find all real solutions: |x - (-20)| = 15 | |x - (-20)| = 15 | -35, -5 | negative thirty-five, negative five | -35, -5 | Final answer is: negative thirty-five, negative five. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-20:15",
"case_id": "x_minus_h_eq_k:-20:15",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-35, -5",
"values": [
-20,
15
],
"final_answer_words": "Final ... | x_minus_h_eq_k:-20:15 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-20:15 | fd3466b11fdf7f33cb83aad377881548924aed6d99e86bcdfb57c392da705c2f | x_minus_h_eq_k:-20:15 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Work through the absolute value cases: |x - (18)| = 13 | |x - (18)| = 13 | 5, 31 | five, thirty-one | 5, 31 | Final answer is: five, thirty-one. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:18:13",
"case_id": "x_minus_h_eq_k:18:13",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "5, 31",
"values": [
18,
13
],
"final_answer_words": "Final answe... | x_minus_h_eq_k:18:13 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:18:13 | 728ecb6f4380c5469586e13d762886182f0b62ade641dcaee2cd2599b3c6a543 | x_minus_h_eq_k:18:13 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve for x: |x - (9)| = 9 | |x - (9)| = 9 | 0, 18 | zero, eighteen | 0, 18 | Final answer is: zero, eighteen. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:9:9",
"case_id": "x_minus_h_eq_k:9:9",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "0, 18",
"values": [
9,
9
],
"final_answer_words": "Final answer is: ... | x_minus_h_eq_k:9:9 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:9:9 | c7689d989ea2f3300e5d45a098002d4b62d05c856bacccee5fbbe08bf4fabd84 | x_minus_h_eq_k:9:9 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve the absolute value equation: |x - (3)| = 7 | |x - (3)| = 7 | -4, 10 | negative four, ten | -4, 10 | Final answer is: negative four, ten. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:3:7",
"case_id": "x_minus_h_eq_k:3:7",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-4, 10",
"values": [
3,
7
],
"final_answer_words": "Final answer is:... | x_minus_h_eq_k:3:7 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:3:7 | 55b205cf9160083840be9e1ea55b9c80b60e9913077eadca197b3f36e06f98c6 | x_minus_h_eq_k:3:7 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Find all real solutions: |x - (18)| = 5 | |x - (18)| = 5 | 13, 23 | thirteen, twenty-three | 13, 23 | Final answer is: thirteen, twenty-three. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:18:5",
"case_id": "x_minus_h_eq_k:18:5",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "13, 23",
"values": [
18,
5
],
"final_answer_words": "Final answer ... | x_minus_h_eq_k:18:5 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:18:5 | 1b09b25ed9163355be50ddd811f5fedbaffe11d24cb91543513992ef3c828ec0 | x_minus_h_eq_k:18:5 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Work through the absolute value cases: |x - (-16)| = 0 | |x - (-16)| = 0 | -16 | negative sixteen | -16 | Final answer is: negative sixteen. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-16:0",
"case_id": "x_minus_h_eq_k:-16:0",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-16",
"values": [
-16,
0
],
"final_answer_words": "Final answer ... | x_minus_h_eq_k:-16:0 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-16:0 | fae4200a1f2e660ff9eb487a8c4e440bbc779c6046493d9d97b0e470c1bb20e7 | x_minus_h_eq_k:-16:0 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve for x: |x - (-14)| = 12 | |x - (-14)| = 12 | -26, -2 | negative twenty-six, negative two | -26, -2 | Final answer is: negative twenty-six, negative two. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-14:12",
"case_id": "x_minus_h_eq_k:-14:12",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-26, -2",
"values": [
-14,
12
],
"final_answer_words": "Final ... | x_minus_h_eq_k:-14:12 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-14:12 | e22a7cbc72b6ad72b9c78f3548a1b7afa79e709b9eae02e51602e6407d5e6e73 | x_minus_h_eq_k:-14:12 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Solve the absolute value equation: |x - (-8)| = 2 | |x - (-8)| = 2 | -10, -6 | negative ten, negative six | -10, -6 | Final answer is: negative ten, negative six. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-8:2",
"case_id": "x_minus_h_eq_k:-8:2",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-10, -6",
"values": [
-8,
2
],
"final_answer_words": "Final answer... | x_minus_h_eq_k:-8:2 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-8:2 | 95f1156694a00008058ddfcad0edad744c496dfa6707111b39a04a556acd1f8b | x_minus_h_eq_k:-8:2 |
algebra.absolute_value_equations | algebra | core_algebra | level_1 | level_1 | Find all real solutions: |x - (-15)| = 5 | |x - (-15)| = 5 | -20, -10 | negative twenty, negative ten | -20, -10 | Final answer is: negative twenty, negative ten. | {
"family": "x_minus_h_eq_k",
"level_number": 1,
"structured": true,
"canonical_key": "x_minus_h_eq_k:-15:5",
"case_id": "x_minus_h_eq_k:-15:5",
"family_id": "x_minus_h_eq_k",
"template_id": "x_minus_h_eq_k",
"final_answer": "-20, -10",
"values": [
-15,
5
],
"final_answer_words": "Final an... | x_minus_h_eq_k:-15:5 | x_minus_h_eq_k | x_minus_h_eq_k | x_minus_h_eq_k:-15:5 | ff4b719dbc20489044bb40159332cfa9f0e46eabae42d83a178f122af98fe6d8 | x_minus_h_eq_k:-15:5 |
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