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# Inequalities

Inequalities are statements of the form:

The following are a set of properties for inequalities:

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.

# Examples

Note: For examples of graphing an inequality, see questions #2 and #3 in Additional Examples at the bottom of the page.

# Absolute Value

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 line.

# Absolute Value & Inequalities

The properties listed below describe how to solve inequalities that contain absolute values.

# Examples

Note: For a more complex example of solving an absolute inequality, see question #1 in the Additional Examples section below.

1 | Solve the inequality
2 | Graph the region determined by the inequality
3 | Graph the region determined by the parabolic inequality

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COURSE HOMEPAGES
MATH 1036
MATH 1037

FACULTY HOMEPAGES
Alex Karassev
Ted Chase