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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

Which value verifies the equation 2x+3=112x+3=11?

Please select an answer first.

Correct answer: A

The correct answer is 4.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Substitute x = 4: 2(4) + 3 = 11, so the equation is true.
  3. Check the conclusion: The correct choice is 4.

Substitute x = 4: 2(4) + 3 = 11, so the equation is true.

2. QuestionMultiple choice

Solve 4(x−2)=2x+84(x-2)=2x+8

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: Distribute to get 4x - 8 = 2x + 8, so 2x = 16 and x = 8.
  3. Check the conclusion: The correct choice is 8.

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

3. QuestionMultiple choice

Three consecutive integers have a sum of 45. What is the greatest integer?

Please select an answer first.

Correct answer: C

The correct answer is 16.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Let the integers be n, n + 1, and n + 2. Then 3n + 3 = 45 gives n = 14, so the greatest is 16.
  3. Check the conclusion: The correct choice is 16.

Let the integers be n, n + 1, and n + 2. Then 3n + 3 = 45 gives n = 14, so the greatest is 16.

4. QuestionMultiple choice

A rectangle has a perimeter of 50 units and width 9 units. What is its length?

Please select an answer first.

Correct answer: D

The correct answer is 16 units.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Use 2l + 2(9) = 50. Then 2l = 32, so l = 16.
  3. Check the conclusion: The correct choice is 16 units.

Use 2l + 2(9) = 50. Then 2l = 32, so l = 16.

5. QuestionMultiple choice

Three consecutive even integers have a sum of 42. What is the smallest integer?

Please select an answer first.

Correct answer: A

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: Let the integers be n, n + 2, and n + 4. Then 3n + 6 = 42, so n = 12.
  3. Check the conclusion: The correct choice is 12.

Let the integers be n, n + 2, and n + 4. Then 3n + 6 = 42, so n = 12.

6. QuestionMultiple choice

Adult tickets cost $8 and student tickets cost $5. If 12 tickets cost $81, how many were adult tickets?

Please select an answer first.

Correct answer: B

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: Let a be adult tickets. Then 8a + 5(12 - a) = 81, so 3a = 21 and a = 7.
  3. Check the conclusion: The correct choice is 7.

Let a be adult tickets. Then 8a + 5(12 - a) = 81, so 3a = 21 and a = 7.

7. QuestionMultiple choice

A car travels at 60 miles per hour. How long does it take to travel 210 miles?

Please select an answer first.

Correct answer: C

The correct answer is 3.5 hours.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Use t = d/r = 210/60 = 3.5 hours.
  3. Check the conclusion: The correct choice is 3.5 hours.

Use t = d/r = 210/60 = 3.5 hours.

8. QuestionMultiple choice

A phone plan costs $25 plus $0.10 per message. How many messages cost $37?

Please select an answer first.

Correct answer: D

The correct answer is 120.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Solve 25 + 0.10m = 37. Then 0.10m = 12, so m = 120.
  3. Check the conclusion: The correct choice is 120.

Solve 25 + 0.10m = 37. Then 0.10m = 12, so m = 120.

9. QuestionMultiple choice

Two workers complete a job in 4 hours and 6 hours individually. How long would they take together?

Please select an answer first.

Correct answer: A

The correct answer is 125\frac{12}{5} hours.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Their combined rate is 1/4 + 1/6 = 5/12 job per hour, so time is 12/5 hours.
  3. Check the conclusion: The correct choice is 125\frac{12}{5} hours.

Their combined rate is 1/4 + 1/6 = 5/12 job per hour, so time is 12/5 hours.

10. QuestionMultiple choice

A number decreased by 18 is 2 less than twice the number. What is the number?

Please select an answer first.

Correct answer: B

The correct answer is -16.

  1. Identify the equation or inequality: Determine the variable, operations, equality or inequality sign, and any context or formula involved.
  2. Isolate and verify: Write n - 18 = 2n - 2. Subtract n and add 18 to get 0 = n + 16, so n = -16.
  3. Check the conclusion: The correct choice is -16.

Write n - 18 = 2n - 2. Subtract n and add 18 to get 0 = n + 16, so n = -16.

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