question
stringlengths 12
86
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stringclasses 31
values | how_to_solve
stringlengths 8
96
| answer
stringlengths 1
24
|
|---|---|---|---|
What is -3^2?
|
Evaluate the integer exponent.
|
Multiply -3 by itself 2 times (0th power = 1).
|
9
|
Factor the polynomial: x^3 - 11x^2 + 35x - 25
|
Factor cubic into linear integer factors if possible.
|
Find integer roots and factor as (x - r1)(x - r2)(x - r3).
|
(x - 5)(x - 1)(x - 5)
|
Solve for x: 3x^2 + 9x + 0 = 0
|
Quadratic with integer roots and non-unit leading coefficient.
|
Factor or use quadratic formula; roots are integers.
|
0, -3
|
Solve for x: 1(x + 14) = 24
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
10
|
Solve for x: sqrt(6x + 160) = 10
|
Radical equation; return integer solution if it exists.
|
Square both sides to get ax + b = c^2, then solve.
|
-10
|
Simplify 18/6
|
Reduce the fraction to simplest form.
|
Divide numerator and denominator by their GCD and normalize sign.
|
3
|
What is 221 ÷ -17?
|
Divide evenly (negative allowed).
|
Divide 221 by -17.
|
-13
|
Solve for x: (-9/9)x + -4 = 68
|
Linear equation with fractional coefficient.
|
Subtract c then multiply by b/a (watch sign).
|
-72
|
Solve the system:
5x + 3y = -8
-2x + -2y = -4
|
Find integer x and y that satisfy both equations.
|
Use substitution or elimination.
|
x=-7, y=9
|
Solve for x: 1x^3 + 6x^2 + -1x + -30 = 0
|
Cubic polynomial factorable to (x - r1)(x - r2)(x - r3).
|
Find integer root by rational root theorem then factor.
|
2, -3, -5
|
Solve for x: 1x^3 + -4x^2 + -11x + 30 = 0
|
Cubic polynomial factorable to (x - r1)(x - r2)(x - r3).
|
Find integer root by rational root theorem then factor.
|
2, -3, 5
|
What is -319 ÷ -29?
|
Divide evenly (negative allowed).
|
Divide -319 by -29.
|
11
|
Find smallest non-negative x such that 20x ≡ 8 (mod 24)
|
Solve linear congruence.
|
Use gcd and modular inverse on reduced modulus (if solution exists).
|
4
|
What is 154 ÷ -22?
|
Divide evenly.
|
Divide 154 by -22.
|
-7
|
What is -238 ÷ 14?
|
Divide evenly.
|
Divide -238 by 14.
|
-17
|
Solve for x: -7x + 12 = 131
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
-17
|
Solve the system:
-5x + 2y = 5
1x + -3y = 25
|
Find integer x and y that satisfy both equations.
|
Use substitution or elimination.
|
x=-5, y=-10
|
Find smallest non-negative x such that -15x ≡ 0 (mod 9)
|
Solve linear congruence.
|
Use gcd and modular inverse on reduced modulus (if solution exists).
|
0
|
Find smallest non-negative x such that 1x ≡ 11 (mod 12)
|
Solve linear congruence.
|
Use gcd and modular inverse on reduced modulus (if solution exists).
|
11
|
Solve for x: (5/12)x + 7 = 37
|
Linear equation with fractional coefficient.
|
Subtract c then multiply by b/a (watch sign).
|
72
|
What is 57 ÷ -19?
|
Divide evenly (negative allowed).
|
Divide 57 by -19.
|
-3
|
Solve for x: log base 2 of x = 1
|
Compute x from the log equation (integer-safe).
|
x = 2^1.
|
2
|
Solve for x: (5x + 62)/(3x + -6) = -1
|
Rational equation that reduces to a linear equation.
|
Cross-multiply to get linear equation and solve for x (ensure denominator ≠ 0).
|
-7
|
Simplify: 3x + 7x + 3y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
10x + 3y
|
Convert the improper fraction 22/11 to a mixed number.
|
Convert to mixed number and simplify the fractional part.
|
Divide numerator by denominator to get whole part and remainder; simplify remainder/denominator.
|
2
|
Solve for x: sqrt(-4x + 40) = 8
|
Radical equation; return integer solution if it exists.
|
Square both sides to get ax + b = c^2, then solve.
|
-6
|
What is 144% of 25?
|
Compute the percent value (integer-safe).
|
Compute 144/100 × 25.
|
36
|
What is -3^4?
|
Evaluate the integer exponent.
|
Multiply -3 by itself 4 times (0th power = 1).
|
81
|
Solve: |-5x + 9| ≤ 11
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
0 ≤ x ≤ 4
|
Solve for x: (-6/12)x + -4 = 32
|
Linear equation with fractional coefficient.
|
Subtract c then multiply by b/a (watch sign).
|
-72
|
Solve for x: 4^x = 16
|
Solve the exponential equation for integer x.
|
Find x such that repeated multiplication of 4 yields 16.
|
2
|
Convert the improper fraction 230/11 to a mixed number.
|
Convert to mixed number and simplify the fractional part.
|
Divide numerator by denominator to get whole part and remainder; simplify remainder/denominator.
|
20 10/11
|
Factor the polynomial: 1x^2 + 6x + 9
|
Factor quadratic into integer linear factors.
|
Find integers r1 and r2 such that polynomial = (x - r1)(x - r2).
|
(x - -3)(x - -3)
|
Solve: 9x + 6 ≤ -93
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≤ -11
|
What is -216 ÷ 24?
|
Divide evenly.
|
Divide -216 by 24.
|
-9
|
Solve for x: -6x + -29 = -143
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
19
|
What is -113 mod 10 (remainder after division)?
|
Compute remainder when a is divided by b.
|
Divide -113 by 10 and take the integer remainder 0..9.
|
7
|
What is -7 × -50?
|
Multiply the numbers.
|
Multiply -7 by -50.
|
350
|
Solve: 7x + -9 ≤ -114
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≤ -15
|
Solve for x: 1x^3 + 0x^2 + -19x + -30 = 0
|
Cubic polynomial factorable to (x - r1)(x - r2)(x - r3).
|
Find integer root by rational root theorem then factor.
|
-2, 5, -3
|
What is -15 ÷ 15?
|
Divide evenly (negative allowed).
|
Divide -15 by 15.
|
-1
|
Solve: -1x + 14 < 8
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x < 6
|
Solve: -10x + 11 ≤ 61
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≤ -5
|
Find one integer solution to 9x + 4y = -35
|
Linear Diophantine equation (return one integer pair).
|
Find any particular solution (here constructed).
|
x=-3, y=-2
|
Solve for x: log base 2 of x = 2
|
Compute x from the log equation (integer-safe).
|
x = 2^2.
|
4
|
Solve for x: -3(x + 12) = 3
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-13
|
What is 114 mod 4 (remainder after division)?
|
Compute remainder when a is divided by b.
|
Divide 114 by 4 and take the integer remainder 0..3.
|
2
|
Solve: |3x + 12| = 15
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
1, -9
|
What is 90 + 105?
|
Add the two numbers.
|
Add 90 and 105.
|
195
|
If each item costs 15 dollars and the total cost is 270, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
18
|
Solve for x: 2x^2 - 22x + 60 = 0
|
Solve the quadratic equation with integer roots.
|
Factor or use quadratic formula (should factor cleanly).
|
5, 6
|
Solve for x: 1x^3 + -6x^2 + 5x + 12 = 0
|
Cubic polynomial factorable to (x - r1)(x - r2)(x - r3).
|
Find integer root by rational root theorem then factor.
|
4, -1, 3
|
Solve for x: 3x^2 + 15x + -18 = 0
|
Quadratic with integer roots and non-unit leading coefficient.
|
Factor or use quadratic formula; roots are integers.
|
1, -6
|
Solve for x: (8/4)x + 10 = -38
|
Linear equation with fractional coefficient.
|
Subtract c then multiply by b/a (watch sign).
|
-24
|
Solve for x: log base 3 of x = 6
|
Compute x from the log equation (integer-safe).
|
x = 3^6.
|
729
|
What is 143 - -197?
|
Subtract the second number from the first.
|
Subtract -197 from 143.
|
340
|
Convert the improper fraction 39/7 to a mixed number.
|
Convert to mixed number and simplify the fractional part.
|
Divide numerator by denominator to get whole part and remainder; simplify remainder/denominator.
|
5 4/7
|
Solve: |-1x + -16| ≤ 16
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-32 ≤ x ≤ 0
|
What is -1^4?
|
Evaluate the integer exponent.
|
Multiply -1 by itself 4 times (0th power = 1).
|
1
|
What is 101% of 200?
|
Compute the percent value (integer-safe).
|
Compute 101/100 × 200.
|
202
|
Simplify 45/9
|
Reduce the fraction to simplest form.
|
Divide numerator and denominator by their GCD and normalize sign.
|
5
|
What is -51 - -174?
|
Subtract the second number from the first.
|
Subtract -174 from -51.
|
123
|
Simplify 30/5
|
Reduce the fraction to simplest form.
|
Divide numerator and denominator by their GCD and normalize sign.
|
6
|
Solve for x: 2x^2 + 10x - 28 = 0
|
Solve the quadratic equation with integer roots.
|
Factor or use quadratic formula (should factor cleanly).
|
2, -7
|
Solve for x: 2^x = 1
|
Solve the exponential equation for integer x.
|
Find x such that repeated multiplication of 2 yields 1.
|
0
|
What is -221 ÷ 13?
|
Divide evenly.
|
Divide -221 by 13.
|
-17
|
Simplify -55/5
|
Reduce the fraction to simplest form.
|
Divide numerator and denominator by their GCD and normalize sign.
|
-11
|
Find smallest non-negative x such that -17x ≡ 1 (mod 12)
|
Solve linear congruence.
|
Use gcd and modular inverse on reduced modulus (if solution exists).
|
7
|
What is 0 ÷ -10?
|
Divide evenly (negative allowed).
|
Divide 0 by -10.
|
0
|
Simplify 15/5
|
Reduce the fraction to simplest form.
|
Divide numerator and denominator by their GCD and normalize sign.
|
3
|
What is 14 - 36?
|
Subtract the second number from the first.
|
Subtract 36 from 14.
|
-22
|
Factor the polynomial: x^3 - 7x^2 + 2x - -40
|
Factor cubic into linear integer factors if possible.
|
Find integer roots and factor as (x - r1)(x - r2)(x - r3).
|
(x - 5)(x - 4)(x - -2)
|
Solve for x: -4(x + 15) = -44
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-4
|
Solve: |-4x + -4| ≤ 13
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-4 ≤ x ≤ 2
|
If each item costs 7 dollars and the total cost is -77, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-11
|
Solve for x: log base 3 of x = 3
|
Compute x from the log equation (integer-safe).
|
x = 3^3.
|
27
|
Convert the improper fraction 9/1 to a mixed number.
|
Convert to mixed number and simplify the fractional part.
|
Divide numerator by denominator to get whole part and remainder; simplify remainder/denominator.
|
9
|
Solve the system:
-3x + 3y = 21
2x + 1y = -23
|
Find integer x and y that satisfy both equations.
|
Use substitution or elimination.
|
x=-10, y=-3
|
Solve for x: 1x^3 + 11x^2 + 39x + 45 = 0
|
Cubic polynomial factorable to (x - r1)(x - r2)(x - r3).
|
Find integer root by rational root theorem then factor.
|
-3, -5, -3
|
Solve: 8x + 16 > -32
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x > -6
|
Solve for x: (5x + -20)/(-7x + -4) = 0
|
Rational equation that reduces to a linear equation.
|
Cross-multiply to get linear equation and solve for x (ensure denominator ≠ 0).
|
4
|
Solve: |-1x + 6| ≤ 5
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
1 ≤ x ≤ 11
|
Solve for x: -4x^2 + -40x + -96 = 0
|
Quadratic with integer roots and non-unit leading coefficient.
|
Factor or use quadratic formula; roots are integers.
|
-6, -4
|
If each item costs 7 dollars and the total cost is -42, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
-6
|
Solve for x: -3x^2 + -9x + 0 = 0
|
Quadratic with integer roots and non-unit leading coefficient.
|
Factor or use quadratic formula; roots are integers.
|
0, -3
|
Convert the improper fraction 4/2 to a mixed number.
|
Convert to mixed number and simplify the fractional part.
|
Divide numerator by denominator to get whole part and remainder; simplify remainder/denominator.
|
2
|
Solve for x: 1x + 29 = 40
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
11
|
What is 0 ÷ 27?
|
Divide evenly.
|
Divide 0 by 27.
|
0
|
Solve: |-6x + -1| = 13
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
2
|
Solve for x: 2^x = 16
|
Solve the exponential equation for integer x.
|
Find x such that repeated multiplication of 2 yields 16.
|
4
|
What is 57 × -7?
|
Multiply the numbers.
|
Multiply 57 by -7.
|
-399
|
Solve for x: -2x^2 + 30x - 112 = 0
|
Solve the quadratic equation with integer roots.
|
Factor or use quadratic formula (should factor cleanly).
|
7, 8
|
What is 2^3?
|
Evaluate the integer exponent.
|
Multiply 2 by itself 3 times (0th power = 1).
|
8
|
Solve for x: 4x + 11 = 15
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
1
|
Convert the improper fraction 29/2 to a mixed number.
|
Convert to mixed number and simplify the fractional part.
|
Divide numerator by denominator to get whole part and remainder; simplify remainder/denominator.
|
14 1/2
|
Solve for x: 8(x + 7) = 176
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
15
|
Find smallest non-negative x such that 18x ≡ 0 (mod 6)
|
Solve linear congruence.
|
Use gcd and modular inverse on reduced modulus (if solution exists).
|
0
|
What is 6^5?
|
Evaluate the integer exponent.
|
Multiply 6 by itself 5 times (0th power = 1).
|
7776
|
If each item costs -3 dollars and the total cost is -90, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
30
|
Simplify -18/2
|
Reduce the fraction to simplest form.
|
Divide numerator and denominator by their GCD and normalize sign.
|
-9
|
End of preview. Expand
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All Mathematical Reasoning-125000
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Contents
addsubmuldivlinear_eqtwo_step_eqfractionexponentinequalityword_algebraquadraticsystem_2x2abs_eqpercentmodsimplify_exprmixed_fractionneg_divlinear_fraction_eqrational_eqquadratic_nonunitcubic_int_rootsystem_3x3diophantineexponential_eqlog_eqradical_eqcongruence_modabsolute_ineqpolynomial_factor
Synthetic algebra-heavy math reasoning dataset.
Each row:
- question
- problem
- how_to_solve
- answer
Useage
Licensed under MIT Free to use for everyone ##Notes It is
- Better to use smaller variants of this dataset for finetuning
- Better to use very small variants of this dataset for evaluation
- Better to use large variants of this dataset for pre-training
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