Algebra 1 Common Core Student Edition, Grade 8-9

How do you w rite
in te r v a l n o ta tio n as
an inequality?
It may help to read its
meaning aloud first.
[-4 , 6 ) means all real
num bers g re a te r th a n
o r equal to - 4 and less
than 6.

You can use an inequality such as x ^ - 3 to describe a p o rtio n of th e n u m b e r line

called a n interval. You can also u se interval notation to describe an interval on th e

number line. In te rv a l n o ta tio n includes th e u se of th ree special symbols. These

sym bols include

parentheses: Use (or) w h en a < or > symbol indicates th a t th e interval's endpoints

are not included.

brackets: Use [ or ] w h e n a ^ or > symbol indicates th a t th e interval’s endpoints

are i n c l u d e d.

infinity: Use °° w h en th e interval co n tin u es forever in a positive direction.

Use - oo w h en th e interval co n tin u es forever in a negative directio n.

Inequality

x> 2

x< 2

1 < x s 5

x<-3 orr>4

Gr ap h

H h

-3 -2 -1

*—I----- 1 b

-3 -2 -1

H ©----1-

H 1-

-1

H h

-I—►

-6 -4 -2

Int erval Notation

[2; °°)

(-00,2)

(1,5]

(- 00 , - 3 ) or [ 4 ,oo)

(IIe SSD Using Interval Notation

Q What is the graph of [ —4 , 6 )? How do you write [ —4 , 6 ) as an inequality?

The bracket indicates th a t

• 4 is included. So use a
  closed circle a t - 4.

The parenthesis indicates

that 6 is not included. So

use an open circle a t 6.

Shade between

-4 and 6.

The inequality - 4 ^ x < 6 rep resen ts th e interval n o tatio n [ - 4 , 6).

O What is the graph of x ^ — 1 o r x > 21 How do you write x ^ — 1 or .r > 2 in

interval notation?

I I " H---- 0 —H----b

-4 -3 -2 -1 0 1 2 3 4

The interval n o tatio n ( - oo, - 1] or (2, oo) rep resen ts th e inequality r<-lorx>2.

G o t It? 5. a. W hat is th e graph of (—2, 7]? How do you w rite (—2,7] as a n inequality?

b. W hat is th e graph of y > 71 How do you w rite y > 7 in interval notation?

G

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