Algebra 1 Common Core Student Edition, Grade 8-9

(Marvins-Underground-K-12) #1
``Objective To solve tw o-step equations in one variable``

``````To get s ta rte d , think
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