Algebra 1 Common Core Student Edition, Grade 8-9

Objective To solve tw o-step equations in one variable

To get s ta rte d , think

about the simpler

case in which you have

ju st one chest of

money.

* f | ■' G e t t i n g R e a d y!

is

The diagram shows the amount of money that each player starts with

in a video g a m e. T o b e f a i r , e a c h p la y e r should have t h e sam e am o u n t

of money. I f each chest contains the same amount of money, how

much money must be in each chest? How do you know?

MATHEMATICAL

PRACTICES

Player 1

g n o

Wi 11

■ 5 " 8 j

' A* 11

I? «

l« n

Player 2

v7 C l v1

v? <10 v5 vl

0" O v 2

Solving Two-Step

Equations

@ Common Core State Standards

A-REI.B.3 Solve linear equations and inequalities

in one variable, including equations w ith coefficients

represented by letters. Also A-CED.A.1, A-REI.A.1

MP2, MP 3,MP4

The problem in th e Solve It can be m o d eled by an equation. The equations in this lesson

are different from th e equations in Lesson 2-1 because they require two steps to solve.

Essent ial Und er st and ing To solve tw o-step equations, you can use the

properties of equality a n d inverse operations to form a series of sim pler equivalent

equations. You can use th e properties of equality repeatedly to isolate th e variable.

A tw o-step equation, like th e one show n below, involves two operations.

Multiplication Addition

2x + 3 = 15

To solve a tw o-step equation, identify th e operations an d u n d o th e m using inverse

operations. You can u n d o th e operations in th e reverse order of the order of operations.

For example, to solve 2x + 3 = 15, you can use subtraction first to u n d o the addition,

a n d th e n use division to u n d o th e m ultiplication.

88 Chapter 2 Solving Equations