#1
Simplify the expression: 3x + 2y - (x - 4y)
2x + 6y
ExplanationCombine like terms and distribute the negative sign.
#2
If 2x + 3 = 5, what is the value of x?
1
ExplanationSubtract 3 from both sides and divide by 2.
#3
If 3(x + 2) = 2(2x - 1), what is the value of x?
-5
ExplanationDistribute, combine like terms, and solve for x.
#4
Find the value of x in the equation: 2(x - 1) + 5 = 3x + 2
1
ExplanationDistribute, combine like terms, and solve for x.
#5
Factorize the quadratic expression: x^2 - 5x + 6
(x - 2)(x - 3)
ExplanationFind two numbers whose sum is the middle coefficient and product is the constant term.
#6
Solve the equation for x: 2(x - 4) = 3x + 5
-13
ExplanationDistribute, combine like terms, and isolate x.
#7
Expand and simplify the expression: (2x - 3)^2
4x^2 - 12x + 9
ExplanationApply the square of a binomial formula.
#8
If 4x - 3 = 5x + 2, what is the value of x?
-3
ExplanationIsolate x by combining like terms and solving.
#9
Find the product: (2x - 5)(3x + 4)
6x^2 + 7x - 20
ExplanationApply the distributive property and combine like terms.
#10
Solve the inequality: 3x + 5 > 2x - 1
x > -6
ExplanationSubtract 2x from both sides and simplify the inequality.
#11
Factorize the expression: 8x^2 - 2
(2x + 1)(2x - 1)
ExplanationFactor out the greatest common factor and apply the difference of squares formula.
#12
Solve for x: |2x - 7| = 3
x = 5/2
ExplanationConsider both cases when the expression inside the absolute value is positive and negative.
#13
Solve for x: |2x - 7| = 11
x = 9
ExplanationConsider both cases when the expression inside the absolute value is positive and negative.
#14
Factorize the following expression: x^2 - 4
(x - 2)(x + 2)
ExplanationApply the difference of squares formula to factorize.
#15
Simplify the expression: (3x^2 - 2x + 5) - (x^2 + 3x - 1)
2x^2 - 5x + 6
ExplanationCombine like terms and subtract the second expression.
#16
Solve the equation for x: 2(x + 3) = 4x - 5
-3
ExplanationDistribute, combine like terms, and isolate x.
#17
Factorize the quadratic expression: 6x^2 - 13x + 6
(2x - 3)(3x - 2)
ExplanationFind two numbers whose sum is the middle coefficient and product is the constant term.
#18
If a + 2b = 10 and 3a - b = 8, what is the value of a?
3
ExplanationSolve the system of equations by elimination or substitution.
#19
Solve the system of equations:
2x + y = 8
x - 3y = -5
x = 2, y = 4
ExplanationUse elimination or substitution to find the values of x and y.
#20
If a - b = 7 and a^2 - b^2 = 33, what are the values of a and b?
a = 6, b = -1
ExplanationSolve the system of equations to find the values of a and b.
#21
Simplify the expression: (4x^3 + 2x^2 - 6x) / 2x
2x^2 + x - 3
ExplanationDivide each term by 2x and simplify the expression.
#22
If 2^(x-1) = 8, what is the value of x?
3
ExplanationWrite 8 as a power of 2 and solve for the exponent.
#23
Simplify: (4a^2b^3)^2
16a^4b^6
ExplanationApply the power of a product rule and simplify the expression.
#24
If 2x - 5 = 3y + 7 and x + 2y = 12, what is the value of x + y?
13
ExplanationSolve the system of equations and find the sum of x and y.
#25
If 4a + 7 = 3b - 2 and 2a - b = 5, what is the value of a + b?
8
ExplanationSolve the system of equations and find the sum of a and b.