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Solving One-Variable Equations

Lesson 7


Write and solve multi-step equations to represent situations, including variables on both sides of the equation.

Common Core Standards

Core Standards


  • 8.EE.C.7 — Solve linear equations in one variable.

Foundational Standards


  • 7.EE.B.4

Criteria for Success


  1. Use expressions and equations to model and solve real-world situations (MP.4).
  2. De-contextualize a situation to represent it algebraically, and re-contextualize to interpret the solution in context of the problem (MP.2).
  3. Build fluency in solving equations with rational numbers and equations on one or both sides of the equation. 

Tips for Teachers


The following tools may be useful for this lesson: calculators.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 or 2 (benefit from worked examples) and Anchor Problem 3 (can be done independently). Find more guidance on adapting our math curriculum for remote learning here.

Fishtank Plus

Subscribe to Fishtank Plus to unlock access to additional resources for this lesson, including:

  • Problem Set
  • Student Handout Editor
  • Google Classrom Integration
  • Vocabulary Package


Anchor Problems


Problem 1

You have a coupon worth $18 off the purchase of a scientific calculator. At the same time, the calculator is offered with a discount of 15%, but no further discounts may be applied. For what tag price on the calculator do you pay the same amount for each discount?

Guiding Questions

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Illustrative Mathematics Coupon versus Discount

Coupon versus Discount, accessed on Aug. 31, 2017, 2:12 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 2

You and your brother go to the same store to buy fruit. You purchase a large watermelon for $7.71 and 2.4 pounds of red grapes. Your brother buys a platter of pre-cut fruit for $9.95 and 1.6 pounds of red grapes. The two of you spend the same amount of money. How much do the grapes cost per pound?

Guiding Questions

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Problem 3

Solve the equations for the variable.

a.    $${-4.2x+6-8.3x={1\over2}(-9x+4)}$$

b.    $${{{5-x}\over8} = {{{1\over4}x-5}\over3}}$$

Guiding Questions

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Problem Set


With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Start each student with a multi-step equation; each student completes one line in the solution of the equation and then passes to the next student; the next student checks the first line and then completes the next line in the solution; this continues until a solution is found and then the next student checks the answer using substitution.
  • Include additional application problems similar to the Anchor Problems and Target Task.

Target Task


Melanie is looking for a summer job. After a few interviews, she ends up with two job offers.

  • Blue Street Café pays $11.75 per hour plus $33 from tips each week. 
  • Fashion Icon Factory Store pays $14.50 per hour with no tips.


1.     If Melanie plans to work 10 hours per week, which job offer should she take to maximize her earnings?

2.     What if Melanie works 20 hours per week?

3.     How many hours would Melanie need to work in order for the pay at each job to be the same? Write and solve an equation.

Mastery Response


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