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.
- x ≥ 5
- x < 1
- x ≤ 4
- x ≥ –10
- x ≤ –2
- x > 9
- x < –8^
- x > ^1
2
EXAMPLE
PRACTICE
Give the interval notation for the inequality.