Grade 8 · Math

8th grade Equations with x on both sides, including no solution or infinitely many worksheet

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Equations with x on both sides, including no solution or infinitely many

Grade 8 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Jun gets 6x + 7 = 3x + 1, and the answer is below zero. What is x?
Kira has to spread first in 3(x + 1) = x + 19. What is x?
Milo faces 4(x − 1) = 2x + 16 with brackets on one side. What is x?
Noah solves 2.5x + 1 = 0.5x + 13 on the decimal sheet. What is x?
Ren has decimals on both bars in 2.5x − 2 = 0.5x + 16. What is x?
6.
Tala spreads the bracket in 2(x + 3) = 2x + 6. How many solutions does it have?
- Exactly one solution
- No solution
- Infinitely many solutions
7.
Ari faces 4(x + 1) = 4x + 9 on paper, with a bracket on the left. How many solutions does it have?
- No solution
- Infinitely many solutions
- Exactly one solution
8.
Jun tests four values for 5x + 3 = 3x + 19. Which value of x makes it true?
- 11
- 16
- 8
- 2
9.
Kira checks four guesses for 7x − 2 = 5x + 10. Which value of x makes it true?
- 4
- 1
- 6
- 12
10.
Luz has four possible answers for 3(x − 4) = x + 8. Which value of x makes it true?
- 6
- 10
- 5
- 20

8th grade Equations with x on both sides, including no solution or infinitely many worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Equations with x on both sides: one, none or infinitely many solutions. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can solve an equation with x on both sides, like 6x + 1 = 3x + 13, by taking the same x pieces off both bars, then the plain piece, then splitting.
I can tell if an equation has one solution, no solution, or infinitely many: after the x pieces cancel, a false statement (-2 = 5) means none, a true one (4 = 4) means every number works.
I can find the number that makes both sides match for every x, and I can solve a story where two plans start apart and meet.

Standard: 8.EE.C.7a, 8.EE.C.7b

Words to know

solution: A number that makes both sides of the equation equal.

no solution: No number makes both sides equal, whatever x is.

infinitely many solutions: Every number makes both sides equal.

like terms: Pieces of the same kind: the x pieces together, the plain numbers together.

bar model (tape diagram): Two bars of equal value: the left side on top, the right side below.

check: Put your answer into both sides and see that they match.

Common mistakes

Your child added the x pieces from the two sides instead of taking the same x pieces off both.

Your child added the plain number when it had to come off, or took it off when it had to go back on.

Your child got the right size of answer but the wrong sign. Try putting the answer into both sides of the equation together and see whether they match.

What to say

Ask: when the same pieces come off both bars, which bar stays equal?

Ask: to get the x pieces alone, does this number come off or go back on?

Questions parents ask

What is the most common mistake with equations with x on both sides, including no solution or infinitely many?

Your child added the x pieces from the two sides instead of taking the same x pieces off both.

How can I help my child with equations with x on both sides, including no solution or infinitely many?

Ask: when the same pieces come off both bars, which bar stays equal?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

See all grade 8 math

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