Digits, Grade 8, Volume 1, Homework Helper

6-2: Writing and Solving Equations with Variables on Both Sides

Key Concept

When you write an equation, you set two expressions equal to each other.

When you solve an equation, you find the value of the variable that makes the two expressions equal.

2x + 6 = -3x + 1. There is a variable term on each side of the equation, 2x and -3x.

Sometimes, both expressions contain a variable term.

table with 2 rows and 2 columns , row1 column 1 , 2 x minus 2 x plus 6 , column 2 equals negative 3 x minus 2 x plus 1 , row2 column 1 , 6 , column 2 equals negative 5 x plus 1 , end table

To solve this kind of equation, bring all of the variable terms to the same side of the equation.

table with 2 rows and 2 columns , row1 column 1 , 2 x plus 3 x plus 6 , column 2 equals negative 3 x plus 3 x plus 1 , row2 column 1 , 5 x plus 6 , column 2 equals 1 , end table

Part 1

Intro

You can use algebra tiles to model equations with integer coefficients and variables on both sides of the equation.

Example Using Models to Solve Equations With Variables on Both Sides

What is the value of x when the expression 6x − 9 equals the expression 4x + 3?

Solution

Use algebra tiles to solve the equation 6x − 9 = 4x + 3. Begin by representing the two expressions.


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Table of Contents

Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties