Algebra 1 Common Core Student Edition, Grade 8-9

Solving Equations W ith

Variab es on Both Sides

Common Core State Standards

A-CED.A.1 Create equations... in one variable and use

them to solve problems. Include equations arising from

lin e a r... functions. Also A-REI.A.1, A-REI.B.3

MP 1, MP 2, MP 3, MP4

Objectives To solve equations w ith variables on b o th sides

To identify eq u atio n s th at are identities or have no solution

TOWN B

POPULATION: 3 300

TOWN A

POPULATION: 3225

Getting Ready!

The diag

After ho know?

You could make a

table to help you

model a solution to

this problem.

MATHEMATICAL

PRACTICES

Yearly growth:

100 people each year

Yearly growth:

75 people each year

Lesson

Vocabulary

identity

The problem in th e Solve It can be m od eled by an equ atio n th at has variables on

both sides.

Es s e n t i a l U n d e r s t a n d i n g To solve equations with variables on b o th sides, you

can use the properties of equality an d inverse operations to write a series of sim pler

equivalent equations.

How do you get

started?

There are variable terms

on b o th sides o f th e

equation. Decide which

variable term to add

or subtract to get the

variable on one side only.

Problem 1 Solving an Equation W ith Variables on Both Sides

What is the solution of 5x + 2 = 2x + 14?

5x + 2 = 2x + 14

2x Subtract 2x from each side.

Simplify.

Subtract 2 from each side.

Simplify.

D iv id e ea ch s id e b y 3.

Simplify.

5x + 2 — 2x = 2x + 14

3x + 2 = 14

3 x + 2 - 2 = 14-2

3x= 12

3x ■ 12

3 3

x = 4

Check 5x + 2 = 2x + 14

5(4) + 2 ^ 2(4) + 14

22 = 22

Substitute 4 for x.

Simplify. The solution checks.

102 Chapter 2 Solving Equations