Algebra Demystified 2nd Ed

Chapter 9 linear inequaliTieS 319

EXAMPLE

x < 3 (–Ç, 3)

x > –6 (–6, Ç)

x ≤ 100 (–Ç, 100]

x≥ 4 [4, Ç)

The relationship between an unbounded inequality, its interval notation,
and its region on the number line is summarized in Figure 9-19.

FIgure 9-19

Inequality Number Line Region Interval Notation

x < a (–∞, a)

(–∞, a]

(a, ∞)

[a, ∞)

x ≤ a

x > a

x ≥ a

a

a

a

a

Ordinarily the variable is written on the left in an inequality but not always.
For instance to say that x is less than 3 (x < 3) is the same as saying 3 is
greater than x (3 > x).

PRACTICE
Give the interval notation for the inequality.

1. x ≥ 5


2. x < 1


3. x ≤ 4


4. x ≥ –10


5. x ≤ –2


6. x > 9


7. x < –8^


8. x > ^1
   2

EXAMPLE

PRACTICE
Give the interval notation for the inequality.