# Solving One-Variable Equations

## Objective

Define a solution to an equation. Solve and check solutions to 1 and 2 step equations.

## Common Core Standards

### Core Standards

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

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• 6.EE.B.5

• 6.EE.B.7

• 7.EE.B.4

## Criteria for Success

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1. Define and understand a solution to an equation as a number or numbers for a variable that make the equation a true statement.
2. Use substitution to check and verify solutions to equations, simplifying first where relevant.
3. Use inverse operations to solve 1 and 2 step equations with rational numbers.

## Tips for Teachers

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• This lesson is approaching 8.EE.7. Students should have a firm grasp on solving 1 and 2 step equations by the end of 7th grade. If needed, review concepts around solving equations in this lesson so students are prepared to solve and model with multi-step equations in upcoming lessons.
• The idea of “solution” is something that students will develop and build on over the course of this year. In this unit, they study solutions as they relate to single-variable equations. They will revisit solutions when they study linear equations in two variables, and then again as they relate to systems of equations.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

Given the equation ${4+15x=49}$,

a.    Is ${x=2}$ a solution to the equation?

b.    Is ${x=3}$ a solution to the equation?

#### References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 3Example 1

Grade 8 Mathematics > Module 4 > Topic A > Lesson 3 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 2

Determine if ${-\frac{1}{2}}$ is a solution to the equation ${-2x+8+6x=-4(x-1)}$.

### Problem 3

Solve each equation. Then check your solution to confirm it is correct.

a.    ${\frac{4}{3}-m= \frac{5}{3}}$

b.    ${-(11-p)=-20}$

c.    ${6.8=-5.4+2n}$

## Problem Set

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

• Procedural practice solving 1 and 2 step equations with rational numbers

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### Problem 1

Is $8$ a solution to ${\frac{1}{2}x+9=13}$?

#### References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 3Exit Ticket

Grade 8 Mathematics > Module 4 > Topic A > Lesson 3 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 2

Write 2 different equations that have ${x=5}$ as a solution.

#### References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 3Exit Ticket

Grade 8 Mathematics > Module 4 > Topic A > Lesson 3 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 3

Is ${-3}$ a solution to the equation ${3x-5=4+2x}$? Explain.

#### References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic A > Lesson 3Exit Ticket

Grade 8 Mathematics > Module 4 > Topic A > Lesson 3 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..

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