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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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5 Tests
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1. Test

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 x+9=16x+9=16

Please select an answer first.

Correct answer: A

The correct answer is 7.

  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 9 from both sides: x = 16 - 9 = 7.
  3. Check the conclusion: The correct choice is 7.

Subtract 9 from both sides: x = 16 - 9 = 7.

2. QuestionMultiple choice

Solve 5x=455x=45

Please select an answer first.

Correct answer: B

The correct answer is 9.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Divide both sides by 5 to get x = 45 / 5 = 9.
  3. Check the conclusion: The correct choice is 9.

Divide both sides by 5 to get x = 45 / 5 = 9.

3. QuestionMultiple choice

Solve 3x−4=173x-4=17

Please select an answer first.

Correct answer: C

The correct answer is 7.

  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 4 to get 3x = 21, then divide by 3 to obtain x = 7.
  3. Check the conclusion: The correct choice is 7.

Add 4 to get 3x = 21, then divide by 3 to obtain x = 7.

4. QuestionMultiple choice

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

Please select an answer first.

Correct answer: D

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: Divide by 2 to get x + 3 = 9, then subtract 3 to obtain x = 6.
  3. Check the conclusion: The correct choice is 6.

Divide by 2 to get x + 3 = 9, then subtract 3 to obtain x = 6.

5. QuestionMultiple choice

Solve 4x+7=314x+7=31

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 7 to get 4x = 24, then divide by 4 to obtain x = 6.
  3. Check the conclusion: The correct choice is 6.

Subtract 7 to get 4x = 24, then divide by 4 to obtain x = 6.

6. QuestionMultiple choice

Solve 7−2x=−57-2x=-5

Please select an answer first.

Correct answer: B

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 7 to get -2x = -12, then divide by -2 to obtain x = 6.
  3. Check the conclusion: The correct choice is 6.

Subtract 7 to get -2x = -12, then divide by -2 to obtain x = 6.

7. QuestionMultiple choice

Solve 3(x−2)+4=193(x-2)+4=19

Please select an answer first.

Correct answer: C

The correct answer is 7.

  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 and combine: 3x - 6 + 4 = 19, so 3x = 21 and x = 7.
  3. Check the conclusion: The correct choice is 7.

Distribute and combine: 3x - 6 + 4 = 19, so 3x = 21 and x = 7.

8. QuestionMultiple choice

Solve 5−2(3x−1)=115-2(3x-1)=11

Please select an answer first.

Correct answer: D

The correct answer is −23-\frac{2}{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: Distribute to get 7 - 6x = 11, so -6x = 4 and x = -4/6 = -2/3.
  3. Check the conclusion: The correct choice is −23-\frac{2}{3}.

Distribute to get 7 - 6x = 11, so -6x = 4 and x = -4/6 = -2/3.

9. QuestionMultiple choice

Solve x4+3=8\frac{x}{4}+3=8

Please select an answer first.

Correct answer: A

The correct answer is 20.

  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 x/4 = 5, then multiply by 4 to obtain x = 20.
  3. Check the conclusion: The correct choice is 20.

Subtract 3 to get x/4 = 5, then multiply by 4 to obtain x = 20.

10. QuestionMultiple choice

Solve x−53=7\frac{x-5}{3}=7

Please select an answer first.

Correct answer: B

The correct answer is 26.

  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 both sides by 3 to get x - 5 = 21, then add 5 to obtain x = 26.
  3. Check the conclusion: The correct choice is 26.

Multiply both sides by 3 to get x - 5 = 21, then add 5 to obtain x = 26.

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