Inequalities are statements of the form:
The following are a set of properties for
The solution set of an inequality is the
set of numbers for which the inequality is true. Two inequalities are equivalent
if they have the same solution sets.
Note: For examples of
graphing an inequality, see questions #2 and #3 in Additional Examples
at the bottom of
The absolute value of a real number x can
be thought of as the distance from 0 to x on the real number line.
Absolute value, denoted |x|, is defined as follows:
Note: Absolute value,
|x| is always nonnegative, since it is a distance on the real number
Absolute Value & Inequalities
The properties listed below describe how to solve
inequalities that contain absolute values.
Note: For a more
complex example of solving an absolute inequality, see question #1 in
the Additional Examples section below.
| Solve the inequality
| Graph the region determined by the inequality
| Graph the region determined by the parabolic inequality
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