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Absolute Value Inequalities

Concept:

The size of the expression ax + b, for various values of the parameters a and b, can be compared to fixed numbers c by using the absolute value inequalities |ax + b| > c, |ax + b| < c, |ax + b| ≥ c, and |ax + b| ≤ c. Solving these inequalities supplies all of the possible values of the variable x that make each inequality true. Each of the inequalities can be represented in the Cartesian coordinate system in a meaningful way.