Algebra 1 Common Core Student Edition, Grade 8-9

flunk m
Do you know how
to solve a related
problem?
Yes. You k n o w h o w
to solve the related
equation x - 15 = -
using the Addition
Property of Equality.

Using the Addition Property of Inequality

What are the solutions of x — 15 > - 12? Graph the solutions.

x- 15 > - 12

x — 15 + 15 > -1 2 + 1 5 Add 15 to each side.

x > 3 S i m p l i f y.

I 1 ----- 1 -------1— ©■” ■+"* The s o lu tio n s o f x > 3 are all real numbers qreater than 3.

-101234

G o t It? 1. W hat are th e solutions of n - 5 < -3? G raph th e solutions.

In P roblem 1, how can you check th a t the final inequality x > 3 describes th e solutions

of the original inequality x - 15 > - 1 2? The original inequality has infinitely

m any solutions, so you can n o t check th e m all. However, you can verify th a t th e final

inequality is correct by checking its en d p o in t an d th e direction of th e inequality symbol.

You will do this in Problem 2.

Solving an Inequality and Checking Solutions

What are the solutions of 10 > x — 3? Graph and check the solutions.

^^^T hinkl

You need to isolate x. Undo

The g ra p h o f 13 a x

(or x < 13) contains 1

real numbers to the le ft o f 13.

To check th e e n d p o in t 13 o f

13 > x, m ake sure th a t 13

To check th e in e q u a lity

IUU I IC-V-VJ IJU IU IC /\. U liU U 10 > x - 3

subtraction by adding the same 10 + 3 s : x — 3 + 3

n u m b e r to each side. 13 > x

( o r x < 13) co n ta in s 13 and a ll j;------+-------•-------*-

J

2 4 6 8 10 12 14

10 = x - 3

10 i 13 - 3

is th e s o lu tio n o f th e re la te d 10 = 10

equation 10 = x - 3.

10 > x - 3

symbol o f 1 3 > x, m ake sure 10 > 12-3

th a t a n u m b e r less th a n 13 10 > 9 V

is a s o lu tio n o f th e o rig in a l

inequality.

< 9 G o t It? 2. W hat are th e solutions of m - 11 > - 2? G raph a n d check th e solutions.

172 Ch ap t er 3 So lvin g In eq u al i t i es