question
stringlengths 12
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stringclasses 31
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stringlengths 8
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stringlengths 1
24
|
|---|---|---|---|
What is 7^3?
|
Evaluate the integer exponent.
|
Multiply 7 by itself 3 times (0th power = 1).
|
343
|
Find one integer solution to 6x + 12y = 0
|
Linear Diophantine equation (return one integer pair).
|
Find any particular solution (here constructed).
|
x=10, y=-5
|
If each item costs 0 dollars and the total cost is 0, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
17
|
Solve for x: log base 5 of x = 5
|
Compute x from the log equation (integer-safe).
|
x = 5^5.
|
3125
|
Convert the improper fraction 39/9 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.
|
4 1/3
|
Solve: -2x + -19 < -25
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x < 3
|
Solve for x: (5x + 9)/(-6x + -10) = -1
|
Rational equation that reduces to a linear equation.
|
Cross-multiply to get linear equation and solve for x (ensure denominator ≠ 0).
|
-1
|
Solve for x: -10x + 29 = 109
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
-8
|
What is -50% of 14?
|
Compute the percent value (integer-safe).
|
Compute -50/100 × 14.
|
-7
|
Solve: |7x + 16| ≤ 18
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-4 ≤ x ≤ 0
|
Simplify 8/2
|
Reduce the fraction to simplest form.
|
Divide numerator and denominator by their GCD and normalize sign.
|
4
|
What is 102% of 0?
|
Compute the percent value (integer-safe).
|
Compute 102/100 × 0.
|
0
|
Simplify -160/16
|
Reduce the fraction to simplest form.
|
Divide numerator and denominator by their GCD and normalize sign.
|
-10
|
Factor the polynomial: x^3 - 6x^2 + -7x - -60
|
Factor cubic into linear integer factors if possible.
|
Find integer roots and factor as (x - r1)(x - r2)(x - r3).
|
(x - 4)(x - 5)(x - -3)
|
Solve for x: 2x^2 - 14x - 16 = 0
|
Solve the quadratic equation with integer roots.
|
Factor or use quadratic formula (should factor cleanly).
|
8, -1
|
Solve for x: -2x^2 + 8x + 64 = 0
|
Solve the quadratic equation with integer roots.
|
Factor or use quadratic formula (should factor cleanly).
|
8, -4
|
What is 272 ÷ 16?
|
Divide evenly.
|
Divide 272 by 16.
|
17
|
What is 11 × 8?
|
Multiply the numbers.
|
Multiply 11 by 8.
|
88
|
Factor the polynomial: 1x^2 + -1x + -20
|
Factor quadratic into integer linear factors.
|
Find integers r1 and r2 such that polynomial = (x - r1)(x - r2).
|
(x - 5)(x - -4)
|
Simplify: -1x + -1x + 8y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-2x + 8y
|
Solve the system:
1x + -4y = 7
3x + -5y = 21
|
Find integer x and y that satisfy both equations.
|
Use substitution or elimination.
|
x=7, y=0
|
Find smallest non-negative x such that 6x ≡ 7 (mod 11)
|
Solve linear congruence.
|
Use gcd and modular inverse on reduced modulus (if solution exists).
|
3
|
Solve for x: log base 3 of x = 5
|
Compute x from the log equation (integer-safe).
|
x = 3^5.
|
243
|
Solve for x: (9/12)x + 3 = 57
|
Linear equation with fractional coefficient.
|
Subtract c then multiply by b/a (watch sign).
|
72
|
Simplify: 5x + -6x + -3y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-1x - 3y
|
Solve for x: 3^x = 9
|
Solve the exponential equation for integer x.
|
Find x such that repeated multiplication of 3 yields 9.
|
2
|
Solve: 7x + -2 > 110
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x > 16
|
What is 0 ÷ 15?
|
Divide evenly.
|
Divide 0 by 15.
|
0
|
Solve for x: 4(x + -7) = -88
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-15
|
Solve for x: -3x + -22 = -25
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
1
|
Simplify: 1x + 2x + 2y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
3x + 2y
|
Solve for x: sqrt(3x + 27) = 6
|
Radical equation; return integer solution if it exists.
|
Square both sides to get ax + b = c^2, then solve.
|
3
|
Factor the polynomial: 1x^2 + 3x + 0
|
Factor quadratic into integer linear factors.
|
Find integers r1 and r2 such that polynomial = (x - r1)(x - r2).
|
(x - 0)(x - -3)
|
Solve for x: (4/12)x + -5 = -45
|
Linear equation with fractional coefficient.
|
Subtract c then multiply by b/a (watch sign).
|
-120
|
Solve the system:
1x + -1y + 4z = -21
1x + -2y + 0z = 2
0x + 1y + -3z = 19
|
Find integer x,y,z satisfying the linear system.
|
Use elimination or Cramer's rule (matrix is invertible).
|
x=4, y=1, z=-6
|
Solve: -7x + 5 ≥ 82
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x ≥ -11
|
Find smallest non-negative x such that 9x ≡ 4 (mod 5)
|
Solve linear congruence.
|
Use gcd and modular inverse on reduced modulus (if solution exists).
|
1
|
What is 136% of 250?
|
Compute the percent value (integer-safe).
|
Compute 136/100 × 250.
|
340
|
Solve: |4x + 10| ≤ 15
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-6 ≤ x ≤ 1
|
What is 1^5?
|
Evaluate the integer exponent.
|
Multiply 1 by itself 5 times (0th power = 1).
|
1
|
Solve: |6x + -13| ≤ 17
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
0 ≤ x ≤ 5
|
Solve for x: sqrt(-3x + 76) = 7
|
Radical equation; return integer solution if it exists.
|
Square both sides to get ax + b = c^2, then solve.
|
9
|
Find smallest non-negative x such that 19x ≡ 18 (mod 25)
|
Solve linear congruence.
|
Use gcd and modular inverse on reduced modulus (if solution exists).
|
22
|
Solve for x: 1x^3 + 10x^2 + 31x + 30 = 0
|
Cubic polynomial factorable to (x - r1)(x - r2)(x - r3).
|
Find integer root by rational root theorem then factor.
|
-5, -3, -2
|
What is 3^1?
|
Evaluate the integer exponent.
|
Multiply 3 by itself 1 times (0th power = 1).
|
3
|
Solve the system:
-5x + 5y = 15
-1x + -1y = 7
|
Find integer x and y that satisfy both equations.
|
Use substitution or elimination.
|
x=-5, y=-2
|
What is 36 × 3?
|
Multiply the numbers.
|
Multiply 36 by 3.
|
108
|
Solve: |-8x + 2| ≤ 10
|
Find integer range of x satisfying the absolute inequality.
|
Isolate and produce interval then take integer bounds.
|
-1 ≤ x ≤ 1
|
What is -3 ÷ 3?
|
Divide evenly.
|
Divide -3 by 3.
|
-1
|
Factor the polynomial: 1x^2 + 7x + 6
|
Factor quadratic into integer linear factors.
|
Find integers r1 and r2 such that polynomial = (x - r1)(x - r2).
|
(x - -6)(x - -1)
|
Solve for x: sqrt(-6x + 45) = 9
|
Radical equation; return integer solution if it exists.
|
Square both sides to get ax + b = c^2, then solve.
|
-6
|
Solve for x: -7x + -21 = -35
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
2
|
Solve for x: 12x + -22 = -118
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
-8
|
What is -78 - 67?
|
Subtract the second number from the first.
|
Subtract 67 from -78.
|
-145
|
What is -252 ÷ 21?
|
Divide evenly.
|
Divide -252 by 21.
|
-12
|
Solve for x: 3x^2 - 9x + 6 = 0
|
Solve the quadratic equation with integer roots.
|
Factor or use quadratic formula (should factor cleanly).
|
1, 2
|
Solve for x: 2^x = 2
|
Solve the exponential equation for integer x.
|
Find x such that repeated multiplication of 2 yields 2.
|
1
|
Simplify: 6x + -3x + -7y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
3x - 7y
|
Solve for x: -1x + 20 = 30
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
-10
|
Find smallest non-negative x such that 8x ≡ 4 (mod 12)
|
Solve linear congruence.
|
Use gcd and modular inverse on reduced modulus (if solution exists).
|
2
|
Solve the system:
3x + 1y + 0z = 18
1x + -4y + -4z = -44
1x + 1y + 3z = 28
|
Find integer x,y,z satisfying the linear system.
|
Use elimination or Cramer's rule (matrix is invertible).
|
x=4, y=6, z=6
|
Factor the polynomial: 1x^2 + -6x + 0
|
Factor quadratic into integer linear factors.
|
Find integers r1 and r2 such that polynomial = (x - r1)(x - r2).
|
(x - 6)(x - 0)
|
What is 19% of 900?
|
Compute the percent value (integer-safe).
|
Compute 19/100 × 900.
|
171
|
Solve for x: -8x + 28 = 52
|
Solve the linear equation.
|
Subtract b from both sides, then divide by a.
|
-3
|
Solve: |3x + -1| = 0
|
Find integer solutions x, if any.
|
Set inside equal to ±c and solve both linear equations.
|
no integer solutions
|
Solve the system:
-1x + -3y + 1z = 2
2x + 4y + 4z = -32
-2x + -1y + 0z = 9
|
Find integer x,y,z satisfying the linear system.
|
Use elimination or Cramer's rule (matrix is invertible).
|
x=-4, y=-1, z=-5
|
Solve for x: 4^x = 64
|
Solve the exponential equation for integer x.
|
Find x such that repeated multiplication of 4 yields 64.
|
3
|
What is 104 ÷ -13?
|
Divide evenly.
|
Divide 104 by -13.
|
-8
|
What is 29% of 500?
|
Compute the percent value (integer-safe).
|
Compute 29/100 × 500.
|
145
|
What is 166 mod 28 (remainder after division)?
|
Compute remainder when a is divided by b.
|
Divide 166 by 28 and take the integer remainder 0..27.
|
26
|
Simplify -18/2
|
Reduce the fraction to simplest form.
|
Divide numerator and denominator by their GCD and normalize sign.
|
-9
|
Solve for x: 1x^3 + 13x^2 + 56x + 80 = 0
|
Cubic polynomial factorable to (x - r1)(x - r2)(x - r3).
|
Find integer root by rational root theorem then factor.
|
-4, -5, -4
|
What is -238 - 34?
|
Subtract the second number from the first.
|
Subtract 34 from -238.
|
-272
|
Solve for x: 1x^3 + 3x^2 + -4x + -12 = 0
|
Cubic polynomial factorable to (x - r1)(x - r2)(x - r3).
|
Find integer root by rational root theorem then factor.
|
-3, 2, -2
|
Simplify: 5x + -8x + -3y
|
Combine like terms.
|
Add coefficients of like terms (x with x, y with y).
|
-3x - 3y
|
Convert the improper fraction 112/9 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.
|
12 4/9
|
Solve for x: log base 2 of x = 0
|
Compute x from the log equation (integer-safe).
|
x = 2^0.
|
1
|
Find one integer solution to 11x + 3y = -4
|
Linear Diophantine equation (return one integer pair).
|
Find any particular solution (here constructed).
|
x=-2, y=6
|
Solve for x: sqrt(-6x + 58) = 4
|
Radical equation; return integer solution if it exists.
|
Square both sides to get ax + b = c^2, then solve.
|
7
|
Convert the improper fraction -19/2 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.
|
-9 -1/2
|
What is 231 ÷ 21?
|
Divide evenly.
|
Divide 231 by 21.
|
11
|
Solve for x: (-7/7)x + -13 = -48
|
Linear equation with fractional coefficient.
|
Subtract c then multiply by b/a (watch sign).
|
35
|
What is -13 × 45?
|
Multiply the numbers.
|
Multiply -13 by 45.
|
-585
|
Solve for x: (4/11)x + 9 = 57
|
Linear equation with fractional coefficient.
|
Subtract c then multiply by b/a (watch sign).
|
132
|
Convert the improper fraction 17/8 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 1/8
|
What is 133 ÷ 7?
|
Divide evenly (negative allowed).
|
Divide 133 by 7.
|
19
|
Solve for x: sqrt(2x + 46) = 8
|
Radical equation; return integer solution if it exists.
|
Square both sides to get ax + b = c^2, then solve.
|
9
|
Solve for x: log base 3 of x = 1
|
Compute x from the log equation (integer-safe).
|
x = 3^1.
|
3
|
If each item costs 5 dollars and the total cost is 75, how many items were bought?
|
Solve using algebra.
|
Divide total cost by price per item.
|
15
|
Solve for x: 8(x + -8) = -72
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
-1
|
What is 195 ÷ -13?
|
Divide evenly (negative allowed).
|
Divide 195 by -13.
|
-15
|
Solve for x: -2x^2 + -2x + 4 = 0
|
Quadratic with integer roots and non-unit leading coefficient.
|
Factor or use quadratic formula; roots are integers.
|
1, -2
|
What is 418 ÷ -22?
|
Divide evenly.
|
Divide 418 by -22.
|
-19
|
What is -56 ÷ -8?
|
Divide evenly.
|
Divide -56 by -8.
|
7
|
Solve for x: 4x^2 + -12x + -72 = 0
|
Quadratic with integer roots and non-unit leading coefficient.
|
Factor or use quadratic formula; roots are integers.
|
6, -3
|
What is 240 ÷ 30?
|
Divide evenly.
|
Divide 240 by 30.
|
8
|
What is 4^5?
|
Evaluate the integer exponent.
|
Multiply 4 by itself 5 times (0th power = 1).
|
1024
|
Solve for x: -1(x + 12) = -19
|
Solve a two-step equation.
|
Divide both sides by a, then subtract b.
|
7
|
Solve: 4x + 2 < 70
|
Solve the inequality.
|
Isolate x by subtracting b then dividing by a (flip sign if dividing by negative).
|
x < 17
|
What is -35% of 60?
|
Compute the percent value (integer-safe).
|
Compute -35/100 × 60.
|
-21
|
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