Algebra 1 Common Core Student Edition, Grade 8-9

Absolute Value Equations

and Inequalities

Common Core State Standards

A-CED.A.1 Create equations... in one variable and use

them to solve problems. Include equations arising from

lin e a r... functions. Also A-SSE.A.1b

MP 1, MP 2. MP 3. MP 4

Ob ject ive To solve eq u atio n s a n d inequalities involving absolute value

T h is is tric k y!

Will she be 60 ft

away more than

once?

MATHEMAtlCAL

PRA CTICES

Getting Ready

Not drawn

100 ft t o scale

In the Solve It, Serena's distance from D arius decreases a n d th e n increases. You can use

absolute value to m odel such changes.

Essent ial Und er st and ing You can solve absolute value eq u atio n s an d

inequalities by first isolating th e absolute value expression, if necessary. Then write an

equivalent pair of linear eq u atio n s or inequalities.

Thi nk
How many solutions
does the equation
have?
There are tw o values on
a n u m ber lin e th a t are
7 u nits fro m 0 :7 and - 7.
So th e e q u a tio n has t w o
solutions.

Solving an Absolute Value Equation

What are the solutions of | x | + 2 = 9? Graph and check the solutions.

|x| + 2 = 9

|x| + 2 - 2 = 9 - 2 S u b tra c t 2 fr o m e a c h side.

|x| = 7 Simplify,

x = 7 or x = - 7 Definition of absolute value

I-

-8

Check

-l 1 ----- 1 ----1—

6 - 4 - 2 0

17 1 + 2 — 9

7 + 2 = 9

4 6 8

e— S u b s t i t u t e 7 a n d - 7 f o r x. -7| + 2 = 9

7 + 2 = 9

Got It? 1. What are the solutions of | n | - 5 = - 2? Graph an d check the solutions.

0

Po w er A l g eb r a.co m | L esson 3 -7 Absolute Value Equations and Inequalities^207