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Linear Equations Practice Tests

These Grade 8 Math practice tests cover one-variable linear equations, inverse operations, multi-step solving, distribution, variables on both sides, fractions, decimals, identities, no-solution equations, and real-world applications.

Skills covered

  • Solving one-step and multi-step equations with integer, fraction, and decimal coefficients
  • Using the distributive property and combining like terms
  • Solving equations with variables on both sides and identifying identities or contradictions
  • Checking solutions by substitution and interpreting equations in context
  • Modeling rates, costs, perimeter, savings, distance, temperature, and other situations

How to use these practice tests

Simplify both sides first, perform the same operation on both sides, isolate the variable, and substitute your answer into the original equation to check it.

For more Grade 8 Math practice, return to the Grade 8 Math category.

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5. Test

Grade 8 Linear Equations Practice Tests

Practice Grade 8 Math questions about one-variable linear equations, multi-step solving, fractions, decimals, identities, no-solution equations, and applications.

Choose the best answer for each question. Keep both sides balanced and check the solution in the original equation.

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

A taxi charges a $3 starting fee and $2 per mile. How many miles can a rider travel for $13?

Please select an answer first.

Correct answer: A

The correct answer is 55 miles.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Set up 3+2m=133+2m=13. Subtract 3 and divide by 2 to get m=5m=5.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Set up 3+2m=133+2m=13. Subtract 3 and divide by 2 to get m=5m=5.

2. QuestionMultiple choice

A rectangle has perimeter 30 units and length 10 units. What is its width?

Please select an answer first.

Correct answer: B

The correct answer is 55 units.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Use 2(10)+2w=302(10)+2w=30. Then 20+2w=3020+2w=30, so w=5w=5.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Use 2(10)+2w=302(10)+2w=30. Then 20+2w=3020+2w=30, so w=5w=5.

3. QuestionMultiple choice

A student has $20 and saves $5 each week. After how many weeks will the student have $60?

Please select an answer first.

Correct answer: C

The correct answer is 88 weeks.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Set up 20+5w=6020+5w=60. Subtract 20 and divide by 5 to get w=8w=8.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Set up 20+5w=6020+5w=60. Subtract 20 and divide by 5 to get w=8w=8.

4. QuestionMultiple choice

A temperature is 6 degrees higher than twice a starting temperature and equals 20 degrees. What is the starting temperature?

Please select an answer first.

Correct answer: D

The correct answer is 77 degrees.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Set up 2t+6=202t+6=20. Subtract 6 and divide by 2 to get t=7t=7.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Set up 2t+6=202t+6=20. Subtract 6 and divide by 2 to get t=7t=7.

5. QuestionMultiple choice

A gym charges $15 plus $8 per month. If the total is $55, how many months were paid?

Please select an answer first.

Correct answer: A

The correct answer is 55 months.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Use 15+8m=5515+8m=55. Then 8m=408m=40, so m=5m=5.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Use 15+8m=5515+8m=55. Then 8m=408m=40, so m=5m=5.

6. QuestionMultiple choice

A cyclist travels 60 miles at 12 miles per hour. How many hours does the trip take?

Please select an answer first.

Correct answer: B

The correct answer is 55 hours.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Use 12t=6012t=60. Dividing by 12 gives t=5t=5.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Use 12t=6012t=60. Dividing by 12 gives t=5t=5.

7. QuestionMultiple choice

Three identical notebooks and a $5 folder cost $20. What is the price of one notebook?

Please select an answer first.

Correct answer: C

The correct answer is $5.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Set up 3n+5=203n+5=20. Then 3n=153n=15, so n=5n=5.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Set up 3n+5=203n+5=20. Then 3n=153n=15, so n=5n=5.

8. QuestionMultiple choice

A rectangular garden has perimeter 46 feet and length 15 feet. What is its width?

Please select an answer first.

Correct answer: D

The correct answer is 88 feet.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Use 2(15)+2w=462(15)+2w=46. Then 2w=162w=16, so w=8w=8.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Use 2(15)+2w=462(15)+2w=46. Then 2w=162w=16, so w=8w=8.

9. QuestionMultiple choice

A phone plan charges $25 plus $0.10 per gigabyte. If the bill is $40, how many gigabytes were used?

Please select an answer first.

Correct answer: A

The correct answer is 150150 gigabytes.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Use 25+0.10g=4025+0.10g=40. Then 0.10g=150.10g=15, so g=150g=150.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Use 25+0.10g=4025+0.10g=40. Then 0.10g=150.10g=15, so g=150g=150.

10. QuestionMultiple choice

Which equation represents the statement: four times a number decreased by 7 equals 21?

Please select an answer first.

Correct answer: B

The correct answer is 4x−7=214x-7=21.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Four times a number is 4x4x, and decreased by 7 gives 4x−74x-7.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Four times a number is 4x4x, and decreased by 7 gives 4x−74x-7.

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