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Grade 8 · Math

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

6 printable versionsChallenge Me10 questions · answer keyFree · no account

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

Grade 8 Math Worksheet - Challenge Me

NameDate

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

  1. Ren spreads on both sides of 6(x − 2) = 2(x + 4). What is x?

  2. Ari spreads and joins in 3(x + 2) + x = 4x + 6. How many solutions does it have?

    • Infinitely many solutions
    • No solution
    • Exactly one solution

  3. Jun has a bracket on the right in 5x + 3 = 5(x + 1). How many solutions does it have?

    • Infinitely many solutions
    • Exactly one solution
    • No solution

  4. Milo needs the sides of 2(x − 3) + 10 = 2x + c to match for every x. What number must c be?

  5. Noah wants 5(x + 2) − 4 = 5x + c to be true for every x. What number must c be?

  6. Pia's sprout is 5 cm tall and grows 4 cm a week. The class sprout is 11 cm tall and grows 1 cm a week. After how many weeks are they the same height?

  7. Ren has read 28 pages and reads 2 a day. A friend has read 10 pages and reads 5 a day. After how many days have both read the same number of pages?

  8. Tala starts 5 miles from the park and bikes away at 11 mph. A friend starts 21 miles out and bikes away at 7 mph. After how many hours are both equally far out?

  9. Zee tests four values for 6(x − 4) = 2(x + 8). Which value of x makes it true?

    • 40
    • 10
    • 3
    • 5

  10. Ari checks four guesses for 8x − 5 = 6x + 9. Which value of x makes it true?

    • 7
    • 1
    • 14
    • 2
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8th grade Equations with x on both sides, including no solution or infinitely many worksheet – printable
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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

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