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Linear Equations and Inequalities Practice Tests

These Grade 9 Math practice tests cover one-step and multi-step linear equations, variables on both sides, identities, contradictions, fractions, decimals, compound inequalities, absolute value, number-line graphs, literal equations, formulas, and real-world models.

Skills covered

  • Solving equations with distribution, fractions, decimals, and variables on both sides
  • Recognizing identities, contradictions, no-solution equations, and infinitely many solutions
  • Solving and graphing one-variable, compound, and absolute-value inequalities
  • Rearranging formulas and interpreting slope, rate, cost, distance, and budget models
  • Checking solutions and translating geometric, ticket, work, travel, and number problems

How to use these practice tests

Simplify both sides first, perform the same operation on both sides, reverse the inequality sign when multiplying or dividing by a negative number, and substitute the final answer into the original equation or model.

For more Grade 9 Math practice, return to the Grade 9 Math category.

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Grade 9 Linear Equations and Inequalities Practice Tests

Practice Grade 9 Math questions about multi-step linear equations, equations with variables on both sides, inequalities, absolute value, formulas, and algebraic models.

Choose the best answer. Keep equations balanced, reverse an inequality when dividing by a negative, show formula steps, and verify the result in context.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Solve 5x+2=3x+145x+2=3x+14

Please select an answer first.

Correct answer: A

The correct answer is 6.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Subtract 3x and 2 from both sides: 2x = 12, so x = 6.
  3. Check the conclusion: The correct choice is 6.

Subtract 3x and 2 from both sides: 2x = 12, so x = 6.

2. QuestionMultiple choice

Solve 4x−9=2x+74x-9=2x+7

Please select an answer first.

Correct answer: B

The correct answer is 8.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Subtract 2x and add 9: 2x = 16, so x = 8.
  3. Check the conclusion: The correct choice is 8.

Subtract 2x and add 9: 2x = 16, so x = 8.

3. QuestionMultiple choice

Solve 7−3x=2x−87-3x=2x-8

Please select an answer first.

Correct answer: C

The correct answer is 3.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Add 3x and 8 to both sides: 15 = 5x, so x = 3.
  3. Check the conclusion: The correct choice is 3.

Add 3x and 8 to both sides: 15 = 5x, so x = 3.

4. QuestionMultiple choice

Solve 6(x−1)=2x+146(x-1)=2x+14

Please select an answer first.

Correct answer: D

The correct answer is 5.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Distribute to get 6x - 6 = 2x + 14, so 4x = 20 and x = 5.
  3. Check the conclusion: The correct choice is 5.

Distribute to get 6x - 6 = 2x + 14, so 4x = 20 and x = 5.

5. QuestionMultiple choice

Solve 2(3x+1)=4x+182(3x+1)=4x+18

Please select an answer first.

Correct answer: A

The correct answer is 8.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Distribute to get 6x + 2 = 4x + 18, so 2x = 16 and x = 8.
  3. Check the conclusion: The correct choice is 8.

Distribute to get 6x + 2 = 4x + 18, so 2x = 16 and x = 8.

6. QuestionMultiple choice

What is the solution of 9x−4=9x+29x-4=9x+2?

Please select an answer first.

Correct answer: B

The correct answer is No solution.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Subtracting 9x gives -4 = 2, a contradiction, so no value of x satisfies the equation.
  3. Check the conclusion: The correct choice is No solution.

Subtracting 9x gives -4 = 2, a contradiction, so no value of x satisfies the equation.

7. QuestionMultiple choice

Which equation has infinitely many solutions?

Please select an answer first.

Correct answer: C

The correct answer is 4(x+2)=4x+84(x+2)=4x+8.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: After distribution, both sides are 4x + 8, so the equation is true for every real number.
  3. Check the conclusion: The correct choice is 4(x+2)=4x+84(x+2)=4x+8.

After distribution, both sides are 4x + 8, so the equation is true for every real number.

8. QuestionMultiple choice

Solve x2+x3=10\frac{x}{2}+\frac{x}{3}=10

Please select an answer first.

Correct answer: D

The correct answer is 12.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Multiply by 6 to get 3x + 2x = 60, so 5x = 60 and x = 12.
  3. Check the conclusion: The correct choice is 12.

Multiply by 6 to get 3x + 2x = 60, so 5x = 60 and x = 12.

9. QuestionMultiple choice

Solve 0.5x+3=80.5x+3=8

Please select an answer first.

Correct answer: A

The correct answer is 10.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Subtract 3 to get 0.5x = 5, then divide by 0.5 to obtain x = 10.
  3. Check the conclusion: The correct choice is 10.

Subtract 3 to get 0.5x = 5, then divide by 0.5 to obtain x = 10.

10. QuestionMultiple choice

Solve 23x−5=9\frac{2}{3}x-5=9

Please select an answer first.

Correct answer: B

The correct answer is 21.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Add 5 to get (2/3)x = 14, then multiply by 3/2 to obtain x = 21.
  3. Check the conclusion: The correct choice is 21.

Add 5 to get (2/3)x = 14, then multiply by 3/2 to obtain x = 21.

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