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# Solving One-Variable Equations

## Objective

Justify each step in solving a multi-step equation with variables on one side of the equation.

## Common Core Standards

### Core Standards

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• 8.EE.C.7.A — Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

• 8.EE.C.7.B — Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

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• 7.EE.A.1

• 7.EE.B.4

## Criteria for Success

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1. Understand there is more than one way to approach solving a multi-step equation.
2. Explain why, in the process of solving an equation, each successive form of an equation is equivalent to the one before it.
3. Analyze, critique, and correct where applicable one’s own work and the work of others (MP.3).

## Tips for Teachers

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This lesson may be extended over more than one day to ensure enough time for both analysis of work and procedural practice.

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problems 1 and 2 (benefit from discussion). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

Two students, Pablo and Karla, are solving an equation. The equation and their work is shown below.

${15-3(x-2)+6x=3(13)}$

 Pablo's Work Karla's Work $15-3x+6+6x=3(13)$ $15-3x+6+6x=39$ $15+6-3x+6x=3(13)$ $-3x+6x+15+6=39$ $21+3x=3(13)$ $3x+21=39$ $3(7+x)=3(13)$ $3x=18$ $7+x=13$ $x=6$ $x=6$
1. Explain what Pablo and Karla did in each step of their work.
2. Are Pablo and Karla correct?

### Problem 2

Two more students, Christian and Esther, are solving the same equation. They take a different approach to solving the equation, but they each make an error in the first two lines of their work, shown below.

${15-3(x-2)+6x=3(13)}$

 Christian's Work Esther's Work $12(x-2)+6x=39$ $15-3x-6+6x=39$ $12x-24+6x=39$ $15-6-3x+6x=39$

Explain the error that each student made.

### Problem 3

Solve the equations.

a.    ${-\left ( \frac{1}{2}-15 \right )+\frac{5}{2}x=-2}$

b.    ${\frac{11}{3}=\frac{5}{3}+3\left (\frac{x}{3}+\frac{2}{9} \right )}$

c.    ${2(3m+6)-4(1-2m)=-20}$

## Problem Set

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

• Give each student an equation to solve; then have students swap with a partner. The partner reviews the work and checks the answer, and then solves the equation in a different way.
• Include procedural practice in solving equations, similar to those in Anchor Problem #3.
• Include error analysis problems where students find, explain, and correct the errors.

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### Problem 1

Solve the equation below. For each step, explain why each line of your work is equivalent to the line before it.

${\frac{1}{2}(-12x+4)+5x=\frac{2}{3}(24)}$

### Problem 2

Find and explain the error in the work below.

${15=-3(m-2)-9}$

${15=-3m+6-9}$

${15=-3m-3}$

${12=-3m}$

${m=-4}$

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