Algebra 1 Common Core Student Edition, Grade 8-9

Compound Inequalities

Common Core State Standards

A-REI.B.3 Solve linear equations and inequalities

in one variable, including equations w ith coefficients

represented by letters. Also A-CED.A.1

MP 1, MP 2, MP 3, MP 4

Ob ject ives To solve an d graph inequalities containing the w ord and

To solve an d graph inequalities containing th e w ord or

ft j Getting Ready! X C

What does it

mean th a t th e

number line shows a

range o f values?

The diagram shows t he number of

boxes of oranges that an orange

tree can produce in 1 year. An

orange grower earns $9.50 f or each

b ox o f o r an g es t h a t he sel l s. How

much could the grower expect to

earn in 1 y ear f rom 1 t r ee? Explain

your reasoning.

Average Annual Orange Tree Production

(n u m b e r o f boxes p e r y e a r)

—I--------h*—V-----!------•------- 1 ----»-

0 1 2 3 4 5

t T

1.3 4.0

MATHEMAtlCAL

PRA CTICES

Lesso n

Vocabulary

com pound

in e q u a lity

in te rv a l n o ta tio n

The Solve It involves a value th a t is betw een two n um bers. You can use a c o m p o u n d

inequality to represent this relationship. A com pound inequality consists of two

distinct inequalities joined by the word and o r th e w o rd or.

Esse n t i a l U n d e r st a n d i n g You find th e solutions of a c o m p o u n d inequality

either by identifying w here the solution sets of th e distinct inequalities overlap or by

com bining th e solution sets to form a larger solution set.

The graph of a c o m p o u n d inequality w ith

the word and contains the overlap of the

graphs of th e two inequalities th at form

th e co m p o u n d inequality.

The graph of a c o m p o u n d inequality w ith

the word or c o n t a i n s each graph of the

two inequalities th a t form th e com p o u n d

inequality.

-«— I— 0 — 1—

2 3 4

■H------- 1 -------1—

5 6 7

» x > 3

8

*—4...... 0 ------1—

-3 -2 -1

—I------- 1 ------- 1 -------1— * -

0 1 2 3

2 3 4

------- 1 ------ 0 1

(^5 6 7) i
.... 1 1 0
8
x>3
— 1 —► and
-3 -2 -1
*..... 1 ..... 0 -------h-
0 1 2 3
—1------0— -4.......1'" >
x<
x< -2
-3 -2 -1
You can rewrite a c o m p o u n d inequality involving and as a single inequality. For
instance, in th e inequality above, you can write x ^ 3 an d x < 7 as 3 < x < 7. You read
this as "x is greater th a n or equal to 3 a n d less th a n or equal to 7.” A nother way to read it
is “x is betw een 3 an d 7, inclusive.” In this example, inclusive m e a n s t h e s o l u t i o n s o f t h e
inequality include both 3 an d 7.
200 Chapter 3 So l v i n g I n e q u al i t i e s
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