Solving One-Variable Equations

Lesson 6

Math

Unit 2

8th Grade

Lesson 6 of 12

Objective


Solve equations with variables on both sides of the equal sign.

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. Understand why solving an equation with variables on both sides of the equal sign follows the same rules as solving an equation with variables on one side.
  2. Use inverse operations to solve equations with variables on both sides of the equal sign.
  3. Analyze and fix incorrect solutions to equations. 

Tips for Teachers


  • Solving equations with variables on both sides of the equal sign is new for 8th graders. Though the approach to solving these equations (simplifying, using inverse operations) is the same as what students are used to, there are now more ways that an equation can be solved and additional places where errors may be made (such as combining terms across the equal sign).
  • Continue to emphasize the importance of maintaining balance in the equation through each “move” students make. 
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Anchor Problems

25-30 minutes


Problem 1

The equation $$2x+3=7$$ can be shown using a balance, like below, where each bag contains an unknown number of tiles, $$x$$.

Solving this equation can be shown using the picture by keeping the balance level. The solution below shows $$x=2$$.

a.   Solve $$5x+1=2x+7$$ in two ways: symbolically, the way you usually do with equations, and also with pictures of a balance. Show how each step you take symbolically is shown in the pictures.

b.   Solve the equation $$4x=x+1$$ using pictures and symbols. Discuss any issues that arise.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Solving EquationsParts a-b

Solving Equations, accessed on Aug. 31, 2017, 1:47 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.

Modified by Fishtank Learning, Inc.

Problem 2

The equation below is solved incorrectly three different ways. 

For each solution, find and explain the error(s) that occurred. Then find the correct solution for $$y$$.

$${12-4y=7y+10}$$

Incorrect Solution #1 Incorrect Solution #2 Incorrect Solution #3

$${22=3y}$$

$${7\frac{1}{3}=y}$$

$$12=11y+10$$

$$11y=-2$$

$$y=-\frac{2}{11}$$

$${4y=7y+22}$$

$${-3y=22}$$

$${y=-7\frac{1}{3}}$$

Guiding Questions

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Student Response

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Problem 3

What value for $$x$$ would make the following equation true?

$$20-(3x-9)-2=-(-11x+1)$$

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 6Example 2

Grade 8 Mathematics > Module 4 > Topic A > Lesson 6 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


Three expressions are shown below.

Expression A: $$-\left(8-\frac{1}{2}x\right)$$
Expression B: $$3-1.5x$$
Expression C: $$-2+6x-6$$

Using the expressions in the chart, find the value of $$x$$ in each situation described.

a.   A = C

b.   A + B = C

Student Response

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Additional Practice


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

Next

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

Lesson 7
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Simplifying Expressions and Verifying Solutions

Topic B: Analyzing and Solving Equations in One Variable

Topic C: Analyzing and Solving Inequalities in One Variable

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