Algebra Demystified 2nd Ed

318 algebra De mystif ieD

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FIgure 9-18

–6

Interval Notation

Sometimes, we use interval notation to represent inequalities. The notation for

an interval tells us how far the solution extends to the left and to the right.

From the notation, we can tell whether or not the endpoint(s) belong to the

interval. We begin with unbounded intervals. These intervals involve infinity.

The symbol for positive infinity is “∞,” and “–∞” is the symbol for negative

infinity. These symbols mean that the numbers in the interval are getting larger

in the positive or negative direction. The intervals for the previous problems

are examples of infinite intervals, or unbounded intervals.

An interval consists of, in order, an open parenthesis “(” or open bracket

“[,” a number or “– ∞,” a comma, a number or “∞,” and a closing parenthesis “)”

or closing bracket “].” A parenthesis is used for strict inequalities (x < a and

x > a) and a bracket is used for an “or equal to” inequality (x < a and x > a).

A parenthesis is always used next to an infinity symbol.

TABLE 91

Inequality Interval

x < number (–∞, number)

x > number (number, ∞)

x ≤ number (–∞, number]

x ≥ number [number,∞)