Grade 8 · Math

8th grade Multi-step equations with fractions, decimals and brackets worksheet

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Multi-step equations with fractions, decimals and brackets

Grade 8 Math Worksheet - Challenge Me

NameDate

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

Jun splits a total into equal parts: (x + 2)/3 + 1 = 5. What is x?
Milo finds (x − 1)/5 + 4 = 6 on the bonus board. What is x?
Tala unwraps 22 − 3(x + 1) = -5 very carefully. What is x?
Zee meets a half outside the brackets: (1/2)(x − 4) + 3 = 9. What is x?
Bo faces fourths in (3/4)(x + 4) − 2 = 7. What is x?
Esme buys 3 star sticker sheets and 2 notebooks for the art club. A notebook costs $1 more than a sheet, and the total is $22. How many dollars is one sticker sheet?
Luz's card has the total on the left: 41 = 3(x + 2) + 2x. What is x?
Milo turns 50 = 2(x − 3) + 5x around before solving it. What is x?
9.
Ren checks four guesses for 19 − 2(x + 4) = -3 on paper. Which value of x makes it true?
- 15
- -15
- 7
- 9
10.
Tala has four possible answers for 63 = 3(x + 3) + 3x. Which value of x makes it true?
- 12
- 10
- 18
- 9

8th grade Multi-step equations with fractions, decimals and brackets worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Multi-step equations like 3(x + 2) + 4x = 31. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can join the x pieces, spread a bracket, and join the plain numbers, then undo the rest in order (4x + 7 − x + 2 = 24 is 3x + 9 = 24).
I can solve it with negatives, decimals and fractions, take a bracket away (20 − 2(x + 3) = 4), and undo a fraction bar ((x + 2)/3 + 1 = 5).
I can put my answer back into the equation to check it, and I can solve a story that gives a bracket and another x term.

Standard: 8.EE.C.7b

Words to know

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

distribute (spread): Multiply the number outside the brackets by every term inside.

coefficient: The number multiplying x. In 3x it is 3.

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

undo: Do the opposite: minus undoes plus, divide undoes times.

check: Put your answer back into the equation and see that both sides match.

Common mistakes

Your child added the plain number to the x pieces.

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 found what all the x pieces are worth together and stopped there.

What to say

Ask: which pieces can be joined, the ones with x or the ones without?

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

Ask: that is what all the x pieces make; how much is just one x?

Questions parents ask

What is the most common mistake with multi-step equations with fractions, decimals and brackets?

Your child added the plain number to the x pieces.

How can I help my child with multi-step equations with fractions, decimals and brackets?

Ask: which pieces can be joined, the ones with x or the ones without?

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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