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Multi-Step Equations - Worksheet 9 - 7th Grade

Hard

Solve linear equations by applying the same operation to both sides and check by substitution.

hard: Combine operations or reverse a relationship.

18 problems · 20-30 minutes · Skills: equations, multi-step

About This Worksheet

This hard-level worksheet contains 18 problems designed for 7th Grade students practicing multi-step equations. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Use signed arithmetic, substitute values and read expressions with variables.

  • Solve linear equations by applying the same operation to both sides and check by substitution.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Solve: 5(x + 9) = 70.
Solution Steps:
  1. Undo addition or move variable terms to one side.
  2. Undo multiplication or distribute as needed.
  3. Substitute x = 5 into the original equation to check.
Answer: x = 5
Tip: Check your result using the method in the example before moving to the next question.
1
Solve: 3(x + 2) = 51.
2
Solve: 5(x + 5) = 0.
3
Solve: 2(x + 2) = 28.
4
Solve: 5(x + 6) = -15.
5
Solve: 2(x + 6) = -6.
6
Solve: 7(x + 8) = 63.
7
Solve: 2(x + 3) = 4.
8
Solve: 7(x + 9) = 105.
9
Solve: 2(x + 11) = 30.
10
Solve: 4(x + 7) = -8.
11
Solve: 8(x + 2) = 64.
12
Solve: 6(x + 2) = 54.
13
Solve: 9(x + 9) = 189.
14
Solve: 4(x + 6) = 0.
15
Solve: 2(x + 7) = 34.
16
Solve: 9(x + 11) = 36.
17
Solve: 5(x + 3) = 70.
18
Solve: 3(x + 3) = 45.

Answer Key

1. x = 152. x = -53. x = 124. x = -95. x = -96. x = 17. x = -18. x = 69. x = 410. x = -911. x = 612. x = 713. x = 1214. x = -615. x = 1016. x = -717. x = 1118. x = 12

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Frequently Asked Questions

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What skills does this expressions and equations worksheet cover?

This worksheet focuses on equations, multi-step. It is designed for 7th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 18 problems. It typically takes 20-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.