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Solving for a Variable - Grade 12 Algebra

This worksheet focuses on advanced algebraic techniques for solving equations with one or more variables, including linear, quadratic, and rational equations.

Grade 12 Math AlgebraSolving for a Variable
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Includes

2 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSA.REI.A.1CCSS.MATH.CONTENT.HSA.REI.B.4CCSS.MATH.CONTENT.HSA.REI.A.2

Topics

AlgebraSolving EquationsVariablesGrade 12
7 sections · Free to use · Printable
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Solving for a Variable

Name:

Date:

Score:

Read each question carefully and solve for the indicated variable. Show all your work for full credit.

1. Solve for x: 3(2x - 5) + 4 = 7x - 10

2. Solve for y: (2y + 1)/3 = (y - 2)/2

3. The solutions to the equation x² - 5x + 6 = 0 are x =   or x =  .

4. To solve 2x² + 7x - 4 = 0 using the quadratic formula, the values for a, b, and c are a =  , b =  , and c =  . The solutions are x =   or x =  .

5. Which of the following is the solution for x in the equation 1/(x+1) + 2/(x-1) = 3/(x²-1)?

a

x = 2

b

x = -1

c

x = 0

d

No solution

6. The equation √(x+2) = x has two valid solutions.

T

True

F

False

7. When solving an equation with absolute values, such as |2x - 3| = 7, you should always consider two cases.

T

True

F

False

8. Solve for m in terms of p and q: p = (2m + 3q) / (m - q)

9. Solve for x: √(x + 7) - √(x - 1) = 2

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