Algebra 1 Common Core Student Edition, Grade 8-9

Y o u c a n w r it e a b s o lu te v a lu e in e q u a lit ie s as c o m p o u n d in e q u a lit ie s. T h e g r a p h s b e lo w
s h o w t w o a b s o lu te v a lu e in e q u a lit ie s.
1 < 2

H— I— I— I— I— © - - O H — h

| n — 11 < 2 represents a ll n u m b e rs
with a distance from 1 t h a t is le ss
th a n 2 u n its. So | n — 11 < 2 means
-2 < n — 1 < 2.

| n — 11 >2 r e p r e s e n ts a ll n u m b e r s

with a distance from 1 th a t is greater

th a n 2 u n its. So | n — 1 1 > 2 m eans

n — 1 < — 2 or n — 1 > 2.

Key Concept Solving Absolute Value Inequalities

T o s o lv e a n in e q u a l i t y i n th e f o r m \A \ < b, w here A is a
variable expression and b > 0 , s o lv e t h e c o m p o u n d i n e q u a l i t y
—b < A < b.

T o s o lv e a n in e q u a l i t y i n th e f o r m |i41 > b, w here A is a
variable expression and b > 0 , s o lv e t h e c o m p o u n d i n e q u a l i t y
A < —b o r A > b.

-b

-e -

-o -

S im ila r r u le s a re t r u e f o r |A | < b o r |yl| > b.

Solving an Absolut e Value Inequalit y Involving

W h a t a r e t h e s o l u t i o n s o f 1 8 n | ^ 2 4? G r a p h t h e s o lu t io n s.

The in e q u a lity says th a t

8 n is at least 24 units

from 0 on a number line.

To be at least 24 units

from 0 ,8 n can be less

than or equal to - 2 4

or greater than or equal

to 24.

J

Write

18n | > 2 4

....../

8n - 24 or 8n 2 = 2 4

You need to isolate n.

Undo multiplication by

dividing each side by the

same number.

8n _ - 2 4 8n _ 24

T ~“8~ I I

n^ -3 or n^3

; i • i— i— i— i— i • i >

-4-3-2-10 1 2 3 4

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■| L e s s o n 3 - 7 A b s o l u t e V a l u e E q u a t i o n s a n d I n e q u a l i t i e s — ------ 209