# Algebra 1 Common Core Student Edition, Grade 8-9

(Marvins-Underground-K-12) #1
``Getting Ready!``

``````Try some numbers
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

``````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