[Assistant] Simplify: x^a + x^a.

[Assistant] {"error": 5, "info": "User tried to combine unlike terms."}


[Assistant] Expand: (x+2)^2.

[Assistant] {"error": 5, "info": "User wrote wrong formula."}


[Assistant] Graph feasible region for x + y < = 4.

[Assistant] {"error": 5, "info": "User graphed boundary wrong."}


[Assistant] Explain half-life.

[Assistant] {"error": 5, "info": "User gave unrelated concept."}


[Assistant] Describe inconsistent system.

[User] They have one solution

[Assistant] {"error": 5, "info": "User gave unrelated description."}


[Assistant] Simplify: 2^x 3^x.

[Assistant] {"error": 5, "info": "User multiplied bases incorrectly."}


[Assistant] Solve: x + y = 5, 2x + 2y = 10.

[Assistant] {"error": 5, "info": "User wrote same equation twice."}


[Assistant] Expand: (x+2)^2.

[Assistant] {"error": 5, "info": "User wrote wrong formula."}


[Assistant] Explain exponential decay graph.

[Assistant] {"error": 5, "info": "User described linear instead."}


[Assistant] Describe extraneous solutions.

[Assistant] {"error": 5, "info": "User gave irrelevant concept."}


[Assistant] Rationalize: (1+2).

[Assistant] {"error": 5, "info": "User gave nonsensical expression."}


[Assistant] Rationalize: (1+2).

[Assistant] {"error": 5, "info": "User gave nonsensical expression."}


[Assistant] Describe nature of roots when discriminant > 0.

[Assistant] {"error": 5, "info": "User gave unrelated answer."}


[Assistant] Graph parabola shifted right.

[Assistant] {"error": 5, "info": "User described linear."}


[Assistant] Simplify: a + b.

[Assistant] {"error": 5, "info": "User attempted to combine unlike radicals."}


[Assistant] Describe asymptote for f *( x ) = 1 / x.

[Assistant] {"error": 5, "info": "User gave irrelevant description."}


[Assistant] Simplify: 1/(x+1) + x.

[Assistant] {"error": 5, "info": "User combined inapplicable terms."}


[Assistant] Solve x ^ 2 + 1 = 0.

[Assistant] {"error": 5, "info": "User tried factoring real roots."}


[Assistant] Solve x ^ 2 + 1 = 0.

[Assistant] {"error": 5, "info": "User tried factoring real roots."}


[Assistant] Solve: ( x - 2 ) = - 1.

[Assistant] {"error": 5, "info": "User solved despite negative root."}


[Assistant] Use quadratic formula on 3x ^ 2 + 2x + 1 = 0.

[Assistant] {"error": 5, "info": "User gave wrong formula."}


[Assistant] Describe asymptote for f *( x ) = 1 / x.

[Assistant] {"error": 5, "info": "User gave irrelevant description."}


[Assistant] Identify axis from equation y = ( x + 2 ) ^ 2.

[Assistant] {"error": 5, "info": "User misidentified axis."}


[Assistant] Simplify: (x+2)/(x^2-4).

[Assistant] {"error": 5, "info": "User gave unrelated factorization."}


[Assistant] Graph parabola shifted right.

[Assistant] {"error": 5, "info": "User described linear."}


[Assistant] Simplify: (x)(y).

[Assistant] {"error": 5, "info": "User multiplied inside incorrectly."}


[Assistant] Rational expression: x/(x-1).

[Assistant] {"error": 5, "info": "User gave wrong domain."}


[Assistant] Rational expression: x/(x-1).

[Assistant] {"error": 5, "info": "User gave wrong domain."}


[Assistant] Describe nature of roots when discriminant > 0.

[Assistant] {"error": 5, "info": "User gave unrelated answer."}


[Assistant] Simplify: a + b.

[Assistant] {"error": 5, "info": "User attempted to combine unlike radicals."}


[Assistant] Describe extraneous solutions.

[Assistant] {"error": 5, "info": "User gave irrelevant concept."}


[Assistant] Simplify composite f*(g*(x)).

[Assistant] {"error": 5, "info": "User wrote separate functions."}


[Assistant] Simplify composite f*(g*(x)).

[Assistant] {"error": 5, "info": "User wrote separate functions."}


[Assistant] Write formula for Fibonacci.

[Assistant] {"error": 5, "info": "User mixed up sequence."}


[Assistant] State domain of f *( x ) = 1 / x.

[Assistant] {"error": 5, "info": "User gave range instead."}


[Assistant] Define asymptote in model review.

[Assistant] {"error": 5, "info": "User described intercept."}


[Assistant] Define asymptote in model review.

[Assistant] {"error": 5, "info": "User described intercept."}


[Assistant] Describe end behavior of f *( x ) = x ^ 2.

[Assistant] {"error": 5, "info": "User gave unrelated description."}


[Assistant] Define outlier.

[Assistant] {"error": 5, "info": "User gave unrelated definition."}


[Assistant] Calculate median of 1,3,5,7,9.

[Assistant] {"error": 5, "info": "User gave wrong median."}


[Assistant] Describe end behavior of f *( x ) = x ^ 2.

[Assistant] {"error": 5, "info": "User gave unrelated description."}


[Assistant] Interpret regression slope.

[Assistant] {"error": 5, "info": "User described intercept instead."}


[Assistant] Describe standard deviation.

[Assistant] {"error": 5, "info": "User gave unrelated concept."}


[Assistant] Describe standard deviation.

[Assistant] {"error": 5, "info": "User gave unrelated concept."}


[Assistant] Explain inverse graphically.

[Assistant] {"error": 5, "info": "User mixed up axes."}


[Assistant] Solve: 4p - 8 = 0.

[User] p -

[Assistant] {"error": 5, "info": "Incomplete response - cannot evaluate."}


[Assistant] Simplify: 6a - (2a - 3).

[User] Okay.

[Assistant] {"error": 5, "info": "Non - mathematical response."}


[Assistant] Solve: 3 *( x - 2 ) = 9.

[User] My dog ate my homework.

[Assistant] {"error": 5, "info": "Off - topic response."}


[Assistant] Combine like terms: 2g + 7 - 3g.

[Assistant] {"error": 5, "info": "No response provided."}


[Assistant] Translate: 'the difference of 10 and twice m'.

[User] twice m less 10

[Assistant] {"error": 5, "info": "Response in words, not algebraic expression."}


[Assistant] Write an expression for '4 increased by a number n'.

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] Write an equation of a line parallel to y = 3x - 1 through ( 0, 2 ) .

[User] I like turtles.

[Assistant] {"error": 5, "info": "Off - topic response."}


[Assistant] Convert x - 2y = 8 to slope - intercept form.

[User] y =

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] Find the slope between (0, 0) and (1, 1).

[User] One billion

[Assistant] {"error": 5, "info": "Nonsensical numerical answer."}


[Assistant] State the slope as a fraction when rise = 3 and run = 2.

[User] 3 cm

[Assistant] {"error": 5, "info": "Provided units and omitted denominator - invalid answer."}


[Assistant] Give the slope of the line x = - 4.

[User] m

[Assistant] {"error": 5, "info": "Answered with variable placeholder instead of value."}


[Assistant] Is the slope of y = 0x + 5 equal to zero?

[User] Yes, it's undefined.

[Assistant] {"error": 5, "info": "Contradictory statement - cannot be both zero and undefined."}


[Assistant] Write point - slope form using ( 2, 3 ) and m = 4.

[Assistant] {"error": 5, "info": "Response contains non - mathematical symbols."}


[Assistant] Identify the inequality symbol in 5? 7 if we want a true statement.

[Assistant] {"error": 5, "info": "No response provided."}


[Assistant] Graph x > = 0 on a number line.

[User] My cat is sleeping.

[Assistant] {"error": 5, "info": "Off - topic response."}


[Assistant] Convert (-, 2) to an inequality.

[User] x <

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] State any solution to x > 10.

[User] Purple

[Assistant] {"error": 5, "info": "Nonsensical non - numeric answer."}


[Assistant] Write interval notation for x! = 5.

[User] 5

[Assistant] {"error": 5, "info": "Response doesn't express an interval."}


[Assistant] Does x < = 2 include x = 2?

[User] Yes, but also maybe not.

[Assistant] {"error": 5, "info": "Contradictory answer."}


[Assistant] Use a bracket, parenthesis, or both to show x > = 1.

[Assistant] {"error": 5, "info": "Non - mathematical symbols."}


[Assistant] Identify one vertex of the region bounded by x > = 0, y > = 0, x + y < = 5.

[Assistant] {"error": 5, "info": "No response provided."}


[Assistant] Graph x = 3 on the coordinate plane.

[User] I love pizza.

[Assistant] {"error": 5, "info": "Off - topic response."}


[Assistant] Rewrite y = 2x + 7 for substitution.

[User] y =

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] State any solution to x - y = 0.

[User] Banana

[Assistant] {"error": 5, "info": "Nonsensical non - numeric answer."}


[Assistant] Provide the slope of the line 0x + 4y = 8.

[User] m

[Assistant] {"error": 5, "info": "Variable placeholder instead of value."}


[Assistant] Does the point ( 2,2 ) satisfy x + y = 5?

[User] Yes and no

[Assistant] {"error": 5, "info": "Contradictory answer."}


[Assistant] Graph the system and state the intersection point.

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] Identify the exponent on x in x^3.

[Assistant] {"error": 5, "info": "No response provided."}


[Assistant] Show the next step: x ^ n x = x ^ {n + 1}.

[User] x^{n+2}

[Assistant] {"error": 5, "info": "Incorrect exponent increment."}


[Assistant] Convert 1*10^3 to a power of 10.

[User] 100

[Assistant] {"error": 5, "info": "Incomplete conversion: should be 10 ^ 3 = 1000."}


[Assistant] Simplify x^1.

[User] 1

[Assistant] {"error": 5, "info": "Misunderstanding: x ^ 1 = x, not 1."}


[Assistant] Estimate 3^2 quickly.

[User] 5

[Assistant] {"error": 5, "info": "Incorrect numerical guess."}


[Assistant] Write x^{-1} as a fraction.

[User] x

[Assistant] {"error": 5, "info": "Misinterpretation: should be 1 / x."}


[Assistant] State whether 0^-1 is defined.

[User] Yes

[Assistant] {"error": 5, "info": "Incorrect: 0 ^ { - 1} is undefined."}


[Assistant] Factor 5x + 10 completely.

[Assistant] {"error": 5, "info": "No response provided."}


[Assistant] Expand (x - 1).

[User] I love pizza.

[Assistant] {"error": 5, "info": "Off - topic response."}


[Assistant] Find factors of x^2 + 4x + 3.

[User] (x+)( )

[Assistant] {"error": 5, "info": "Incomplete factoring response."}


[Assistant] State the constant in 7x - 2x + 5.

[User] x

[Assistant] {"error": 5, "info": "Incorrect type; constant is 5."}


[Assistant] Factor 4 - x.

[User] I'm not sure maybe shrug

[Assistant] {"error": 5, "info": "Uncertain / invalid response."}


[Assistant] Expand (x + 6)*(x - 6).

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] What is the degree of 2?

[User] Probably x

[Assistant] {"error": 5, "info": "Response unrelated; degree of constant 2 is 0."}


[Assistant] Solve x^2 + 5x + 6 = 0 by factoring.

[Assistant] {"error": 5, "info": "No response provided."}


[Assistant] Complete the square: x + 4x + 7. First step?

[User] x + 4x + = 7 +

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] State one root of x ^ 2 - 16 = 0.

[User] Blue

[Assistant] {"error": 5, "info": "Nonsensical non - numeric answer."}


[Assistant] What is the vertex of y = x^2?

[User] v

[Assistant] {"error": 5, "info": "Variable placeholder instead of value."}


[Assistant] Does x ^ 2 + 4 = 0 have real roots?

[User] Yes and no

[Assistant] {"error": 5, "info": "Answer should be no; roots are imaginary."}


[Assistant] Write vertex form for y = x^2 + 2x + 1.

[Assistant] {"error": 5, "info": "Non - mathematical symbols."}


[Assistant] Find discriminant of x^2 - 2x + 1.

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] Simplify 36.

[Assistant] {"error": 5, "info": "No response provided."}


[Assistant] Rationalize 2/5. First step?

[User] 2/5

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] Simplify x^2 - 25. State the value.

[User] Green

[Assistant] {"error": 5, "info": "Nonsensical non - numeric answer."}


[Assistant] Simplify: (x^0) * (x^2).

[User] x^0

[Assistant] {"error": 5, "info": "User ignored x^2 factor; result should be x^2."}


[Assistant] Does x = x always?

[User] Yes and no

[Assistant] {"error": 5, "info": "Contradictory answer."}


[Assistant] Simplify (9x).

[Assistant] {"error": 5, "info": "Non - mathematical symbols."}


[Assistant] Solve ( x - 1 ) = 4.

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] Simplify (x - 9)/(x - 3x).

[Assistant] {"error": 5, "info": "No response provided."}


[Assistant] Solve 2 / x = 1.

[User] I like fractions!

[Assistant] {"error": 5, "info": "Off - topic response."}


[Assistant] Add (1/(x - 2)) + (1/(x + 2)). State denominator.

[User] (x - 2)(x + 2)

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] State the excluded value of (x - 1)/(x + 3).

[User] Yellow

[Assistant] {"error": 5, "info": "Nonsensical non - numeric answer."}


[Assistant] Simplify (x/5)/(x/5).

[User] x

[Assistant] {"error": 5, "info": "Incorrect; should be 1."}


[Assistant] Does ( x - 2 ) / ( x - 2 ) = 1 for all x?

[User] Yes and no

[Assistant] {"error": 5, "info": "Contradictory answer."}


[Assistant] Find the vertical asymptote of y = 1 / x.

[Assistant] {"error": 5, "info": "Non - mathematical symbols."}


[Assistant] Solve ( x + 3 ) / ( x - 1 ) = 0.

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] Simplify 2^3 / 2^5.

[Assistant] {"error": 5, "info": "No response provided."}


[Assistant] Solve 3 ^ x = 27.

[User] I like exponents!

[Assistant] {"error": 5, "info": "Off - topic response."}


[Assistant] What is the asymptote of y = 2 ^ x + 4?

[User] y = 4

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] Evaluate 5^2.

[User] Red

[Assistant] {"error": 5, "info": "Nonsensical non - numeric answer."}


[Assistant] Simplify (x^3)^2.

[User] x

[Assistant] {"error": 5, "info": "Incorrect; should be x ^ 6."}


[Assistant] Is 2^x always positive?

[User] Yes and no

[Assistant] {"error": 5, "info": "Contradictory answer."}


[Assistant] Rewrite 4^-1.

[Assistant] {"error": 5, "info": "Non - mathematical symbols."}


[Assistant] Solve 2 ^ ( x + 2 ) = 4.

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] Find the mean of 1, 2, 3.

[Assistant] {"error": 5, "info": "No response provided."}


[Assistant] What is P(A or B) for mutually exclusive events?

[User] I love stats!

[Assistant] {"error": 5, "info": "Off - topic response."}


[Assistant] Find the median of 1, 3, 5. First step?

[User] 3

[Assistant] {"error": 5, "info": "Incomplete response."}


[Assistant] What is the probability of drawing a red card?

[User] Blue

[Assistant] {"error": 5, "info": "Nonsensical non - numeric answer."}


[Assistant] Calculate 4P3.

[User] 4

[Assistant] {"error": 5, "info": "Incorrect; should be 24."}


[Assistant] Are all probabilities equal to 1?

[User] Yes and no

[Assistant] {"error": 5, "info": "Contradictory answer."}


[Assistant] Find the IQR of 2, 4, 6, 8.

[Assistant] {"error": 5, "info": "Non - mathematical symbols."}


[Assistant] Calculate P(A and B) for independent events.

[Assistant] {"error": 5, "info": "Blank response."}


[Assistant] What is the probability of rolling a 6 on a die?

[User] I like dice!

[Assistant] {"error": 5, "info": "Off - topic response."}


[Assistant] Convert 3x - y = 6 to y = 3x - 6.

[User] y = 3x - 6

[Assistant] {"error": 6, "info": "No error: correct form."}


[Assistant] Write y - 1 = 2 *( x - 3 ) from slope 2 intercept 1.

[User] y - 1 = 2 *( x - 3 )

[Assistant] {"error": 6, "info": "No error: correct form."}


[Assistant] Solve: 3x - 2 = 7.

[User] x = 3

[Assistant] {"error": 6, "info": "No error: correct isolation of x."}


[Assistant] Solve: x + 5 > 8.

[User] x>3

[Assistant] {"error": 6, "info": "No error: correct inequality solution."}


[Assistant] Find slope from (0,5) and (5,0).

[User] -1

[Assistant] {"error": 6, "info": "No error: correct slope."}


[Assistant] Simplify: 4x + 3x.

[User] 7x

[Assistant] {"error": 6, "info": "No error: user combined like terms correctly."}


[Assistant] Solve: x / 4 = 5.

[User] x = 20

[Assistant] {"error": 6, "info": "No error: user solved correctly."}


[Assistant] Find y - intercept of y = - 4x + 7.

[User] 7

[Assistant] {"error": 6, "info": "No error: correct intercept."}


[Assistant] Solve: 2x - 1 < = 3.

[User] x < = 2

[Assistant] {"error": 6, "info": "No error: correct solution."}


[Assistant] Find y - intercept of y = - 4x + 7.

[User] 7

[Assistant] {"error": 6, "info": "No error: correct intercept."}


[Assistant] Solve: x+5>8.

[User] x>3

[Assistant] {"error": 6, "info": "No error: correct inequality solution."}


[Assistant] Solve: |x| = 5.

[User] x = 5, - 5

[Assistant] {"error": 6, "info": "No error: both solutions given."}


[Assistant] Solve: |x| = 5.

[User] x = 5, - 5

[Assistant] {"error": 6, "info": "No error: both solutions given."}


[Assistant] Solve: 2x - 1 < = 3.

[User] x < = 2

[Assistant] {"error": 6, "info": "No error: correct solution."}


[Assistant] Solve: 3x - 2 = 7.

[User] x = 3

[Assistant] {"error": 6, "info": "No error: correct isolation of x."}


[Assistant] Graph x > = - 1 on number line.

[User] x > = - 1

[Assistant] {"error": 6, "info": "No error: correct graph."}


[Assistant] Graph x > = - 1 on number line.

[User] x > = - 1

[Assistant] {"error": 6, "info": "No error: correct graph."}


[Assistant] Combine like terms: 2a + 3a.

[User] 5a

[Assistant] {"error": 6, "info": "No error: combined correctly."}


[Assistant] Translate: 'three more than m'.

[User] m + 3

[Assistant] {"error": 6, "info": "No error: correct translation."}


[Assistant] Solve: |x-1|<3.

[User] -2<x<4

[Assistant] {"error": 6, "info": "No error: correct compound inequality."}


[Assistant] Translate: 'three more than m'.

[User] m + 3

[Assistant] {"error": 6, "info": "No error: correct translation."}


[Assistant] Convert 3x - y = 6 to y = 3x - 6.

[User] y = 3x - 6

[Assistant] {"error": 6, "info": "No error: correct form."}


[Assistant] Write y - 1 = 2 *( x - 3 ) from slope 2 intercept 1.

[User] y - 1 = 2 *( x - 3 )

[Assistant] {"error": 6, "info": "No error: correct form."}


[Assistant] Solve: |x-1|<3.

[User] -2<x<4

[Assistant] {"error": 6, "info": "No error: correct compound inequality."}


[Assistant] Combine like terms: 2a + 3a.

[User] 5a

[Assistant] {"error": 6, "info": "No error: combined correctly."}


[Assistant] What is the slope of y = 2x + 3?

[User] 2

[Assistant] {"error": 6, "info": "No error: correct slope."}


[Assistant] Simplify: 4x + 3x.

[User] 7x

[Assistant] {"error": 6, "info": "No error: user combined like terms correctly."}


[Assistant] Write 6e2 in standard form.

[User] 600

[Assistant] {"error": 6, "info": "No error: correct conversion."}


[Assistant] Graph: y = 2x and y = x + 1, find intersection.

[User] (1,3)

[Assistant] {"error": 6, "info": "No error: correct intersection."}


[Assistant] Write 6e2 in standard form.

[User] 600

[Assistant] {"error": 6, "info": "No error: correct conversion."}


[Assistant] Simplify: 9/3^2.

[User] 1

[Assistant] {"error": 6, "info": "No error: correct simplification."}


[Assistant] Simplify: 2^3 * 2^2.

[User] 2^5

[Assistant] {"error": 6, "info": "Correct simplification."}


[Assistant] Solve by elimination: x - y = 2, x + y = 6.

[User] x = 4,y = 2

[Assistant] {"error": 6, "info": "No error: correct elimination."}


[Assistant] Solve: 2x + y = 5 and 4x + 2y = 10.

[User] Infinite solutions

[Assistant] {"error": 6, "info": "No error: dependent system."}


[Assistant] Solve by substitution: y = 3x, x + y = 8.

[User] x = 2,y = 6

[Assistant] {"error": 6, "info": "No error: solved correctly."}


[Assistant] Solve by elimination: x - y = 2, x + y = 6.

[User] x = 4,y = 2

[Assistant] {"error": 6, "info": "No error: correct elimination."}


[Assistant] Multiply: (x+2)(x+4).

[User] x^2+6x+8

[Assistant] {"error": 6, "info": "No error: correct FOIL."}


[Assistant] Factor GCF: 6x^2+9x.

[User] 3x*(2x+3)

[Assistant] {"error": 6, "info": "No error: correct GCF."}


[Assistant] Multiply: (x+2)(x+4).

[User] x^2+6x+8

[Assistant] {"error": 6, "info": "No error: correct FOIL."}


[Assistant] Simplify: x^2 x^3.

[User] x^5

[Assistant] {"error": 6, "info": "No error: correct exponent addition."}


[Assistant] Simplify: (x^4)^2.

[User] x^8

[Assistant] {"error": 6, "info": "No error: correct power rule."}


[Assistant] Factor: x^2+5x+6.

[User] (x+2)(x+3)

[Assistant] {"error": 6, "info": "No error: correct factoring."}


[Assistant] Solve: x + 2y = 4 and x - y = 1.

[User] x = 2,y = 1

[Assistant] {"error": 6, "info": "No error: correct solution."}


[Assistant] Factor: x^2+4x+4.

[User] (x+2)^2

[Assistant] {"error": 6, "info": "No error: correct perfect square."}


[Assistant] Simplify: x^2 x^3.

[User] x^5

[Assistant] {"error": 6, "info": "No error: correct exponent addition."}


[Assistant] Factor: x^2+4x+4.

[User] (x+2)^2

[Assistant] {"error": 6, "info": "No error: correct perfect square."}


[Assistant] Factor: x^2-9.

[User] (x-3)(x+3)

[Assistant] {"error": 6, "info": "No error: correct difference of squares."}


[Assistant] Simplify: 2^-3.

[User] 1/8

[Assistant] {"error": 6, "info": "No error: correct negative exponent."}


[Assistant] Solve: x + 2y = 4 and x - y = 1.

[User] x = 2,y = 1

[Assistant] {"error": 6, "info": "No error: correct solution."}


[Assistant] Simplify: 2^-3.

[User] 1/8

[Assistant] {"error": 6, "info": "No error: correct negative exponent."}


[Assistant] Simplify: (x^4)^2.

[User] x^8

[Assistant] {"error": 6, "info": "No error: correct power rule."}


[Assistant] Factor: x^2-9.

[User] (x-3)(x+3)

[Assistant] {"error": 6, "info": "No error: correct difference of squares."}


[Assistant] Solve by substitution: y = 3x, x + y = 8.

[User] x = 2,y = 6

[Assistant] {"error": 6, "info": "No error: solved correctly."}


[Assistant] Simplify: 9/3^2.

[User] 1

[Assistant] {"error": 6, "info": "No error: correct simplification."}


[Assistant] Factor GCF: 6x^2+9x.

[User] 3x*(2x+3)

[Assistant] {"error": 6, "info": "No error: correct GCF."}


[Assistant] Simplify: (a)^2.

[User] a

[Assistant] {"error": 6, "info": "No error: correct simplification."}


[Assistant] Discriminant of x^2 + 2x + 1.

[User] 0

[Assistant] {"error": 6, "info": "No error: correct discriminant."}


[Assistant] Expand (x+1)^2.

[User] x^2 + 2x + 1

[Assistant] {"error": 6, "info": "No error: correct expansion."}


[Assistant] Rationalize: 1/3.

[User] 3/3

[Assistant] {"error": 6, "info": "No error: correct rationalization."}


[Assistant] Add: 1/4 + 1/4.

[User] 1/2

[Assistant] {"error": 6, "info": "No error: correct addition."}


[Assistant] Simplify: (x^(1/3))^3.

[User] x

[Assistant] {"error": 6, "info": "No error: correct exponent rules."}


[Assistant] Simplify: (16).

[User] 4

[Assistant] {"error": 6, "info": "No error: correct simplification."}


[Assistant] Discriminant of x^2 + 2x + 1.

[User] 0

[Assistant] {"error": 6, "info": "No error: correct discriminant."}


[Assistant] Simplify: (x+5)/(x+5).

[User] 1

[Assistant] {"error": 6, "info": "No error: correct simplification."}


[Assistant] Simplify: (x+5)/(x+5).

[User] 1

[Assistant] {"error": 6, "info": "No error: correct simplification."}


[Assistant] Find vertex of y = x ^ 2 + 4x + 4.

[User] (-2, 0)

[Assistant] {"error": 6, "info": "No error: correct vertex."}


[Assistant] Solve: ( x - 1 ) / ( x + 1 ) = 0.

[User] x = 1

[Assistant] {"error": 6, "info": "No error: correct solution."}


[Assistant] Find vertex of y = x ^ 2 + 4x + 4.

[User] (-2, 0)

[Assistant] {"error": 6, "info": "No error: correct vertex."}


[Assistant] Add: 1/4 + 1/4.

[User] 1/2

[Assistant] {"error": 6, "info": "No error: correct addition."}


[Assistant] Solve: ( x + 2 ) = 5.

[User] x = 23

[Assistant] {"error": 6, "info": "No error: correct solution."}


[Assistant] Use quadratic formula on x ^ 2 - 3x + 2 = 0.

[User] x = 1, 2

[Assistant] {"error": 6, "info": "No error: correct formula application."}


[Assistant] Simplify: (a)^2.

[User] a

[Assistant] {"error": 6, "info": "No error: correct simplification."}


[Assistant] Solve: x ^ 2 - 5x + 6 = 0.

[User] x = 2, 3

[Assistant] {"error": 6, "info": "No error: correct factoring."}


[Assistant] Simplify: (x^(1/3))^3.

[User] x

[Assistant] {"error": 6, "info": "No error: correct exponent rules."}


[Assistant] Simplify: (x^2-9)/(x-3).

[User] x+3

[Assistant] {"error": 6, "info": "No error: correct simplification."}


[Assistant] Simplify: (x^2-9)/(x-3).

[User] x+3

[Assistant] {"error": 6, "info": "No error: correct simplification."}


[Assistant] Use quadratic formula on x ^ 2 - 3x + 2 = 0.

[User] x = 1, 2

[Assistant] {"error": 6, "info": "No error: correct formula application."}


[Assistant] Solve: x ^ 2 - 5x + 6 = 0.

[User] x = 2, 3

[Assistant] {"error": 6, "info": "No error: correct factoring."}


[Assistant] Expand (x+1)^2.

[User] x^2 + 2x + 1

[Assistant] {"error": 6, "info": "No error: correct expansion."}


[Assistant] Rationalize: 1/3.

[User] 3/3

[Assistant] {"error": 6, "info": "No error: correct rationalization."}


[Assistant] Solve: ( x - 1 ) / ( x + 1 ) = 0.

[User] x = 1

[Assistant] {"error": 6, "info": "No error: correct solution."}


[Assistant] Multiply: (2/x)(x/5).

[User] 2/5

[Assistant] {"error": 6, "info": "No error: correct multiplication."}


[Assistant] Multiply: (2/x)(x/5).

[User] 2/5

[Assistant] {"error": 6, "info": "No error: correct multiplication."}


[Assistant] Interpret correlation r = - 1.

[User] perfect negative

[Assistant] {"error": 6, "info": "No error: correct interpretation."}


[Assistant] Compute mean of 2,4,6,8.

[User] mean = 5

[Assistant] {"error": 6, "info": "No error: correct mean."}


[Assistant] Interpret correlation r = - 1.

[User] perfect negative

[Assistant] {"error": 6, "info": "No error: correct interpretation."}


[Assistant] Domain of f *( x ) = 1 / x.

[User] x! = 0

[Assistant] {"error": 6, "info": "No error: correct domain."}


[Assistant] Evaluate g *( f *( x ) ) for f *( x ) = x + 2,g *( x ) = x ^ 2.

[User] g *( f *( x ) ) = ( x + 2 ) ^ 2

[Assistant] {"error": 6, "info": "No error: correct evaluation."}


[Assistant] Given f *( x ) = 2x + 3, find f *( 2 ) .

[User] f *( 2 ) = 7

[Assistant] {"error": 6, "info": "No error: correct evaluation."}


[Assistant] Evaluate g *( f *( x ) ) for f *( x ) = x + 2,g *( x ) = x ^ 2.

[User] g *( f *( x ) ) = ( x + 2 ) ^ 2

[Assistant] {"error": 6, "info": "No error: correct evaluation."}


[Assistant] Compute mean of 2,4,6,8.

[User] mean = 5

[Assistant] {"error": 6, "info": "No error: correct mean."}


[Assistant] Given recursive an = an - 1 + 2,a1 = 5, find a2.

[User] a2 = 7

[Assistant] {"error": 6, "info": "No error: correct recursion."}


[Assistant] Write explicit formula for geometric sequence 3,6,12.

[User] an = 3 * 2 ^ ( n - 1 )

[Assistant] {"error": 6, "info": "No error: correct formula."}


[Assistant] Given f *( x ) = 2x + 3, find f *( 2 ) .

[User] f *( 2 ) = 7

[Assistant] {"error": 6, "info": "No error: correct evaluation."}


[Assistant] Domain of f *( x ) = 1 / x.

[User] x! = 0

[Assistant] {"error": 6, "info": "No error: correct domain."}


[Assistant] Find 5th term of arithmetic sequence a1 = 2,d = 3.

[User] a5 = 14

[Assistant] {"error": 6, "info": "No error: correct term."}


[Assistant] Given recursive an = an - 1 + 2,a1 = 5, find a2.

[User] a2 = 7

[Assistant] {"error": 6, "info": "No error: correct recursion."}


[Assistant] Compose f *( x ) = x + 1,g *( x ) = 2x.

[User] f *( g *( x ) ) = 2x + 1

[Assistant] {"error": 6, "info": "No error: correct composition."}


[Assistant] Find inverse of f *( x ) = x + 4.

[User] f ^ { - 1} ( x ) = x - 4

[Assistant] {"error": 6, "info": "No error: correct inverse."}


[Assistant] Find 5th term of arithmetic sequence a1 = 2,d = 3.

[User] a5 = 14

[Assistant] {"error": 6, "info": "No error: correct term."}


[Assistant] Find inverse of f *( x ) = x + 4.

[User] f ^ { - 1} ( x ) = x - 4

[Assistant] {"error": 6, "info": "No error: correct inverse."}


[Assistant] Solve: 5x + 3 = 18.

[User] Subtract 3 from both sides

[Assistant] {"error": 6, "info": "Correct first step."}


[Assistant] Translate: 'the sum of n and 12'.

[User] n + 12

[Assistant] {"error": 6, "info": "Accurate translation."}


[Assistant] Combine like terms: 6a + 3a.

[User] 9a

[Assistant] {"error": 6, "info": "Correct coefficient addition."}


[Assistant] Distribute: 2*(4 - k).

[User] 8 - 2k

[Assistant] {"error": 6, "info": "Proper application of distributive property."}


[Assistant] Simplify: -(2y - 5).

[User] -2y + 5

[Assistant] {"error": 6, "info": "Signs flipped correctly."}


[Assistant] Translate: 'three times a number minus 4'.

[User] 3x - 4

[Assistant] {"error": 6, "info": "Correct algebraic expression."}


[Assistant] Combine constants: 10 - 3 + 2.

[User] 9

[Assistant] {"error": 6, "info": "Correct simplification of constants."}


[Assistant] Solve: 2 *( 7 - m ) = 0.

[User] Set 7 - m = 0

[Assistant] {"error": 6, "info": "Valid use of zero - product idea."}


[Assistant] Find the slope between (0, 4) and (3, 10).

[User] Difference in y is 6 and difference in x is 3

[Assistant] {"error": 6, "info": "Correct identification of rise and run."}


[Assistant] In y = - 2x + 7, what is b?

[User] 7

[Assistant] {"error": 6, "info": "Correct y - intercept."}


[Assistant] Given y - 5 = - 4 *( x - 2 ) , state the slope.

[User] Slope is -4

[Assistant] {"error": 6, "info": "Correct extraction of slope."}


[Assistant] What is the slope of any line parallel to y = 1 / 4x - 3?

[User] 1/4

[Assistant] {"error": 6, "info": "Correct - parallel lines have equal slopes."}


[Assistant] First step to solve for y in 5x + y = 12?

[User] Subtract 5x from both sides

[Assistant] {"error": 6, "info": "Valid isolation step."}


[Assistant] State the slope of x = 3.

[User] Undefined

[Assistant] {"error": 6, "info": "Correct - vertical line slope is undefined."}


[Assistant] Slope of a line perpendicular to y = - 2x + 1?

[User] 1/2

[Assistant] {"error": 6, "info": "Correct negative reciprocal of - 2."}


[Assistant] Write point-slope form through (-1, 0) with slope 3.

[User] y - 0 = 3 *( x + 1 )

[Assistant] {"error": 6, "info": "Correct point - slope equation."}


[Assistant] Subtract 3 from both sides of x + 3 > 7.

[User] x > 4

[Assistant] {"error": 6, "info": "Correct first step in solving the inequality."}


[Assistant] Divide both sides of -4x < 8 by -4. What is the new inequality?

[User] x > -2

[Assistant] {"error": 6, "info": "Correctly flipped the symbol after dividing by a negative."}


[Assistant] Express x > 5 in interval notation.

[User] (5, )

[Assistant] {"error": 6, "info": "Correct interval notation."}


[Assistant] On a number line for x < -1, should the dot at -1 be open or closed?

[User] Open dot

[Assistant] {"error": 6, "info": "Correct endpoint style for a strict inequality."}


[Assistant] Split |x - 3| < = 4 into two inequalities.

[User] x - 3 < = 4 and x - 3 > = - 4

[Assistant] {"error": 6, "info": "Correct setup for absolute - value < = inequality."}


[Assistant] For y > = 2x - 1, which side of the line should be shaded?

[User] Above (including the line)

[Assistant] {"error": 6, "info": "Correct shading direction and inclusion."}


[Assistant] Combine the solution sets x < -2 or x > 3. How many intervals are there?

[User] Two disjoint intervals

[Assistant] {"error": 6, "info": "Correct understanding of an OR compound inequality."}


[Assistant] Write interval notation for 1 < = x < = 4.

[User] [1, 4]

[Assistant] {"error": 6, "info": "Correct closed interval notation."}


[Assistant] Convert x < = 0 to interval notation.

[User] (-, 0]

[Assistant] {"error": 6, "info": "Correct interval for x < = 0."}


[Assistant] Add the equations 2x - y = 1 and - 2x + y = 3. What do you notice?

[User] They cancel to 0 = 4

[Assistant] {"error": 6, "info": "Correct observation leading to no solution."}


[Assistant] Subtract y = 3x - 2 from y = - x + 6 to set up elimination. What is the resulting equation?

[User] 4x - 8 = 0

[Assistant] {"error": 6, "info": "Correct subtraction: 3x - ( - x ) = 4x and - 2 - 6 = - 8."}


[Assistant] First step in solving by substitution: y = x + 1 and 2x + y = 7.

[User] Replace y with x + 1 in 2x + y = 7

[Assistant] {"error": 6, "info": "Correct substitution setup."}


[Assistant] Identify the slopes of y = 2x + 5 and y = 2x - 3.

[User] Both slopes are 2

[Assistant] {"error": 6, "info": "Correct - parallel lines."}


[Assistant] What region satisfies x + y < = 4 and x > = 0 and y > = 0?

[User] The triangle bounded by axes and the line x + y = 4

[Assistant] {"error": 6, "info": "Correct description of feasible region."}


[Assistant] Solve 3x - y = 4 & 2x + y = 1 by adding the equations.

[User] 5x = 5

[Assistant] {"error": 6, "info": "Correct elimination step before dividing."}


[Assistant] If a system gives back x = 2, how would you find y using y = x - 3?

[User] Plug to get y = - 1

[Assistant] {"error": 6, "info": "Correct substitution result."}


[Assistant] What is the perpendicular slope to x = 4?

[User] 0

[Assistant] {"error": 6, "info": "Correct - horizontal line slope is 0."}


[Assistant] Simplify: x^3 x^2.

[User] x^5

[Assistant] {"error": 6, "info": "Correct application of product rule."}


[Assistant] Simplify: (x^2)^3.

[User] x^6

[Assistant] {"error": 6, "info": "Correct use of power rule."}


[Assistant] Express x^(-3) as a fraction.

[User] 1/x^3

[Assistant] {"error": 6, "info": "Correct negative - exponent conversion."}


[Assistant] What is 7^0?

[User] 1

[Assistant] {"error": 6, "info": "Correct zero - exponent result."}


[Assistant] Convert 4.7*10^2 to standard form.

[User] 470

[Assistant] {"error": 6, "info": "Correct scientific - notation conversion."}


[Assistant] Factor 6x^2 + 9x.

[User] 3x*(2x + 3)

[Assistant] {"error": 6, "info": "Correct GCF factorization."}


[Assistant] Factor x^2 - 36.

[User] (x - 6)(x + 6)

[Assistant] {"error": 6, "info": "Correct difference - of - squares factorization."}


[Assistant] Expand (2x - 3)(x + 2).

[User] 2x + x - 6

[Assistant] {"error": 6, "info": "Correct FOIL and simplification."}


[Assistant] Factor x^2 + 11x + 30.

[User] (x + 5)(x + 6)

[Assistant] {"error": 6, "info": "Correct trinomial factorization."}


[Assistant] Expand (x - 2)(x + 7).

[User] x + 5x - 14

[Assistant] {"error": 6, "info": "Correct multiplication and combination."}


[Assistant] Factor 8x - 18.

[User] 2 *( 4x - 9 ) = 2 *( 2x - 3 )*( 2x + 3 )

[Assistant] {"error": 6, "info": "Correct multi - step GCF and difference - of - squares factoring."}


[Assistant] Find the square of (3x + 1).

[User] 9x + 6x + 1

[Assistant] {"error": 6, "info": "Correct binomial square expansion."}


[Assistant] Factor 25 - y.

[User] (5 - y)(5 + y)

[Assistant] {"error": 6, "info": "Correct difference of squares."}


[Assistant] Expand (x + 9)(x - 2).

[User] x + 7x - 18

[Assistant] {"error": 6, "info": "Correct product and simplification."}


[Assistant] Solve x^2 - 4x + 4 = 0 by factoring.

[User] ( x - 2 )*( x - 2 ) = 0, x = 2

[Assistant] {"error": 6, "info": "Correct factoring and solution."}


[Assistant] What is the discriminant of x^2 - 6x + 9.

[User] 6 - 419 = 0

[Assistant] {"error": 6, "info": "Correct discriminant calculation."}


[Assistant] Complete the square for x + 6x. Add what?

[User] ( 6 / 2 ) = 9

[Assistant] {"error": 6, "info": "Correct number to complete the square."}


[Assistant] Does y = - x + 2 open upward or downward?

[User] Downward

[Assistant] {"error": 6, "info": "Correct identification of parabola direction."}


[Assistant] Solve x^2 + 2x - 3 = 0 by factoring.

[User] ( x + 3 )*( x - 1 ) = 0

[Assistant] {"error": 6, "info": "Correct factors."}


[Assistant] Find the axis of symmetry for y = 3x^2 - 6x + 1.

[User] x = - ( - 6 ) / ( 23 ) = 1

[Assistant] {"error": 6, "info": "Correct axis of symmetry."}


[Assistant] Simplify 32.

[User] 2*2*2*2*2

[Assistant] {"error": 6, "info": "Correct simplification."}


[Assistant] Solve x = 6. Square both sides.

[User] x = 36

[Assistant] {"error": 6, "info": "Correct squaring step."}


[Assistant] Rationalize 3/3.

[User] 33 / 3 = 3

[Assistant] {"error": 6, "info": "Correct rationalization."}


[Assistant] Simplify: x^4 * x^2.

[User] x^6

[Assistant] {"error": 6, "info": "Correct exponent addition."}


[Assistant] Simplify (25x).

[User] 5|x|

[Assistant] {"error": 6, "info": "Correct simplification with absolute value."}


[Assistant] Solve x = 3. Cube both sides.

[User] x = 27

[Assistant] {"error": 6, "info": "Correct cubing step."}


[Assistant] Add 12 + 27. Simplify first.

[User] 23 + 33 = 53

[Assistant] {"error": 6, "info": "Correct addition of like radicals."}


[Assistant] Solve ( x + 2 ) = 5. Square both sides.

[User] x + 2 = 25

[Assistant] {"error": 6, "info": "Correct squaring step."}


[Assistant] Simplify (x - 1)/(x + 1).

[User] x - 1

[Assistant] {"error": 6, "info": "Correct simplification with cancellation."}


[Assistant] Solve 1 / ( x - 2 ) = 3. Multiply by ( x - 2 ) .

[User] 1 = 3 *( x - 2 )

[Assistant] {"error": 6, "info": "Correct multiplication step."}


[Assistant] Find the vertical asymptote of y = 1 / ( x + 4 ) .

[User] x = - 4

[Assistant] {"error": 6, "info": "Correct asymptote identification."}


[Assistant] Add (2/x) + (3/x). Combine terms.

[User] 5/x

[Assistant] {"error": 6, "info": "Correct addition with common denominator."}


[Assistant] Simplify (x - 16)/(x - 4). Factor numerator.

[User] (x - 4)(x + 4)/(x - 4)

[Assistant] {"error": 6, "info": "Correct factoring step."}


[Assistant] Divide (x/2) / (x/4). Rewrite as multiplication.

[User] (x/2)*(4/x)

[Assistant] {"error": 6, "info": "Correct reciprocal step."}


[Assistant] Solve ( x - 1 ) / ( x + 2 ) = 0. Set numerator to zero.

[User] x - 1 = 0, x = 1

[Assistant] {"error": 6, "info": "Correct numerator step."}


[Assistant] Simplify 2^4 2^3.

[User] 2 ^ 7 = 128

[Assistant] {"error": 6, "info": "Correct exponent addition and evaluation."}


[Assistant] Solve 3 ^ x = 9. Rewrite 9.

[User] 9 = 3 ^ 2, so x = 2

[Assistant] {"error": 6, "info": "Correct base matching."}


[Assistant] Evaluate y = 2 ^ x for x = 0.

[User] 2 ^ 0 = 1

[Assistant] {"error": 6, "info": "Correct evaluation."}


[Assistant] Simplify (5^2)^3.

[User] 5^6

[Assistant] {"error": 6, "info": "Correct power rule application."}


[Assistant] Find the horizontal asymptote of y = 3 ^ x + 5.

[User] y = 5

[Assistant] {"error": 6, "info": "Correct asymptote identification."}


[Assistant] Rewrite 2^-3.

[User] 1 / 2 ^ 3 = 1 / 8

[Assistant] {"error": 6, "info": "Correct negative exponent simplification."}


[Assistant] Is y = 0.8 ^ x growth or decay?

[User] Decay

[Assistant] {"error": 6, "info": "Correct identification of decay."}


[Assistant] Solve 4 ^ ( x + 1 ) = 16. Rewrite 16.

[User] 16 = 4 ^ 2, x + 1 = 2

[Assistant] {"error": 6, "info": "Correct base matching step."}


[Assistant] Simplify 3^5 / 3^2.

[User] 3 ^ 3 = 27

[Assistant] {"error": 6, "info": "Correct exponent subtraction."}


[Assistant] Find the y - intercept of y = 2 ^ x - 3.

[User] y = 2 ^ 0 - 3 = - 2

[Assistant] {"error": 6, "info": "Correct y - intercept calculation."}


[Assistant] Find the mean of 5, 10, 15.

[User] ( 5 + 10 + 15 ) / 3 = 10

[Assistant] {"error": 6, "info": "Correct mean calculation."}


[Assistant] Calculate P(4) for a die roll.

[User] 1/6

[Assistant] {"error": 6, "info": "Correct probability calculation."}


[Assistant] Find the median of 2, 4, 6, 8, 10.

[User] 6

[Assistant] {"error": 6, "info": "Correct median identification."}


[Assistant] Compute 4C2.

[User] ( 4 * 3 ) / ( 2 * 1 ) = 6

[Assistant] {"error": 6, "info": "Correct combination calculation."}


[Assistant] Find the range of 1, 3, 5, 7.

[User] 7 - 1 = 6

[Assistant] {"error": 6, "info": "Correct range calculation."}


[Assistant] If P ( A ) = 0.5, P ( B ) = 0.4, independent, find P ( A and B ) .

[User] 0.5 * 0.4 = 0.2

[Assistant] {"error": 6, "info": "Correct independent event probability."}


[Assistant] Find Q1 for 1, 3, 5, 7, 9.

[User] 3

[Assistant] {"error": 6, "info": "Correct first quartile identification."}


[Assistant] Are events A and B mutually exclusive if P ( A and B ) = 0?

[User] Yes

[Assistant] {"error": 6, "info": "Correct mutually exclusive identification."}


[Assistant] Find the IQR of 2, 4, 6, 8, 10.

[User] Q3 - Q1 = 8 - 4 = 4

[Assistant] {"error": 6, "info": "Correct interquartile range calculation."}


[Assistant] Calculate 5P3.

[User] 5 * 4 * 3 = 60

[Assistant] {"error": 6, "info": "Correct permutation calculation."}


[Assistant] Find the median of 1, 2, 3, 4, 5.

[User] 3

[Assistant] {"error": 6, "info": "Correct median identification."}