Algebra 1 Common Core Student Edition, Grade 8-9

Getting Ready!

Try some numbers

to help you construct

a p attern fo r this

problem.

You a re buying movie tic k e ts online fo r a group o f your frie n d s. You

have to en ter th e number o f tickets you want on th e screen shown.

You a re using a d e b it card to pay fo r th e tic k e ts and have a to ta l o f

$45 to spend. How many tickets can you buy? Explain your answer.

MATHEMATICAL

PRACTICES

eoo HE)

Number of tickets you would like to purchase: [

'fiZ j'.b * 'jt.CSr f'tOC.SzCOiJjSJ “ fjbS ChllSC.)-?

* 55.00 ' = $

Solving Multi-Step

Equations

@ Common Core State Standards

A-CED.A.1 Create e q u a tio n s... in one variable and use

them to solve problems. Include equations arising from

linear... functions. Also A-REI.A.1, A-REI.B.3

MP 1, MP 2, MP 3, MP4

Objective To solve m ulti-step equations in o n e variable

In this lesson, you will learn to w rite a n d solve m ulti-step equations.

Essential U nderstanding To solve m ulti-step equations, you form a series of

simpler equivalent equations. To do this, use the properties of equality, inverse operations,

an d properties of real num bers. You use th e p roperties until you isolate th e variable.

How is this equation

Combining Like Terms

What is the solution of 5 = 5m — 23 + 2m?

different from 5 = 5m - 23 + 2m

equations you've

seen before? 5 = 5m + 2m^ — 2 3 Commutative Property of Addition

The variable occurs in 5 = 7m — 2 3 Combine like terms.

two terms. You can

sim plify the equation by

grouping like terms and

combining them.

5 + 23 = 7 m - 23 + 23

28 = 7m^

28 7m

7 7

A dd 23 to each side.

Simplify.

Divide each side by 7.

4 = m Simplify.

Check 5 = 5m — 2 3 + 2m

5 = 5 ( 4 ) - 23 + 2 ( 4 ) Substitute 4 for m.

5 = 5 / S im plify. The s o lu tio n checks.

94 Chapter 2 Solving Equations