Beginning Algebra, 11th Edition

Graphing Intervals on a Number Line

Write each inequality in interval notation, and graph the interval.

(a)

The statement says that xcan represent any number greater than but

cannot equal. The interval is written We graph this interval by placing

a parenthesis at and drawing an arrow to the right, as in FIGURE 19. The parenthe-

sis at - 5 indicates that - 5 is notpart of the graph.

- 5

- 5 1 - 5, q 2.

x7- 5 - 5

x7- 5

EXAMPLE 1

152 CHAPTER 2 Linear Equations and Inequalities in One Variable

–6 –5 –4 –3 –2 –1 0 1 2

–5 is not included.

FIGURE 19Graph of the interval 1 - 5, q 2

(b)

The statement means the same as. The inequality symbol continues

to point toward the lesser number.The graph of written in interval notation

as 1 - q, 3 2 ,is shown in FIGURE 20.

x 6 3,

37 x x 6 3

37 x

–4 –3 –2 –1 041 2 3

FIGURE 20Graph of the interval 1 - q, 3 2 NOW TRY

Keep the following important concepts regarding interval notation in mind:

1.A parenthesis indicates that an endpoint is not includedin a solution set.

2.A bracket indicates that an endpoint is includedin a solution set.

3.A parenthesis is alwaysused next to an infinity symbol, or.

4.The set of all real numbers is written in interval notation as 1 ˆ, ˆ 2.

- q q

NOTE Some texts use a solid circle rather than a square bracket to indicate that

an endpoint is included in a number line graph. An open circle is used to indicate

noninclusion, rather than a parenthesis.

~

The table summarizes methods of expressing solution sets of linear inequalities.

Set-Builder Notation Interval Notation Graph

5 x|xis a real number 6 1 - q, q 2

a

5 x|xÚa 6 3 a, q 2

a

5 x|x 7 a 6 1 a, q 2

a 5 x|x...a 6 1 - q, a 4

a

5 x|x 6 a 6 1 - q, a 2

NOW TRY
EXERCISE 1
Write each inequality in inter-
val notation, and graph the
interval.

(a)x6- 1 (b) - 2 ...x

NOW TRY ANSWERS

(a)

(b)

–3–2–1 0 1 2 3

3 - 2, q 2

–3 –2 –1 0 1 2 3

1 - q, - 12

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