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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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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

How many solutions does 2(x+3)=2x+62(x+3)=2x+6 have?

Please select an answer first.

Correct answer: A

The correct answer is Infinitely many solutions.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Distributing gives 2x+6=2x+62x+6=2x+6, which is true for every real value of xx.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Distributing gives 2x+6=2x+62x+6=2x+6, which is true for every real value of xx.

2. QuestionMultiple choice

How many solutions does 3x+4=3x+93x+4=3x+9 have?

Please select an answer first.

Correct answer: B

The correct answer is No solution.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Subtracting 3x3x gives 4=94=9, a false statement, so there is no solution.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Subtracting 3x3x gives 4=94=9, a false statement, so there is no solution.

3. QuestionMultiple choice

How many solutions does 5(x−2)=5x−105(x-2)=5x-10 have?

Please select an answer first.

Correct answer: C

The correct answer is Infinitely many solutions.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Distributing gives 5x−10=5x−105x-10=5x-10, which is true for every real value of xx.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Distributing gives 5x−10=5x−105x-10=5x-10, which is true for every real value of xx.

4. QuestionMultiple choice

How many solutions does 2x+7=2x+12x+7=2x+1 have?

Please select an answer first.

Correct answer: D

The correct answer is No solution.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Subtracting 2x2x gives 7=17=1, which is false.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Subtracting 2x2x gives 7=17=1, which is false.

5. QuestionMultiple choice

How many solutions does 4x+8=4(x+2)4x+8=4(x+2) have?

Please select an answer first.

Correct answer: A

The correct answer is Infinitely many solutions.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: The right side distributes to 4x+84x+8, so both sides are identical for every xx.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

The right side distributes to 4x+84x+8, so both sides are identical for every xx.

6. QuestionMultiple choice

How many solutions does 6x−2=6x+36x-2=6x+3 have?

Please select an answer first.

Correct answer: B

The correct answer is No solution.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Subtracting 6x6x gives −2=3-2=3, which is false.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Subtracting 6x6x gives −2=3-2=3, which is false.

7. QuestionMultiple choice

How many solutions does x2+1=x2+1\frac{x}{2}+1=\frac{x}{2}+1 have?

Please select an answer first.

Correct answer: C

The correct answer is Infinitely many solutions.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: The two sides are identical, so every real number satisfies the equation.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

The two sides are identical, so every real number satisfies the equation.

8. QuestionMultiple choice

How many solutions does 3(x+1)=3x+43(x+1)=3x+4 have?

Please select an answer first.

Correct answer: D

The correct answer is No solution.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Distributing gives 3x+3=3x+43x+3=3x+4, which reduces to the false statement 3=43=4.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Distributing gives 3x+3=3x+43x+3=3x+4, which reduces to the false statement 3=43=4.

9. QuestionMultiple choice

How many solutions does −2(x−5)=−2x+10-2(x-5)=-2x+10 have?

Please select an answer first.

Correct answer: A

The correct answer is Infinitely many solutions.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: Distributing gives −2x+10=−2x+10-2x+10=-2x+10, an identity true for every real xx.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

Distributing gives −2x+10=−2x+10-2x+10=-2x+10, an identity true for every real xx.

10. QuestionMultiple choice

How many solutions does 7x+1=7x+17x+1=7x+1 have?

Please select an answer first.

Correct answer: B

The correct answer is Infinitely many solutions.

  1. Simplify each side: Use the distributive property and combine like terms before isolating the variable.
  2. Keep the equation balanced: The equation is true for all real values because both sides are the same expression.
  3. Check the solution: Substitute the value into the original equation and confirm that both sides have the same value.

The equation is true for all real values because both sides are the same expression.

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