1-6 Absolute Value Equations and Inequalities

Objective

To write and solve equations and inequalities involving absolute value

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In the Solve It, signed numbers represent distance and direction. Sometimes, only the size of a number (its absolute value), not the direction, is important.

Essential Understanding An absolute value quantity is nonnegative. Since opposites have the same absolute value, an absolute value equation can have two solutions.

An absolute value equation has a variable within the absolute value sign. For example, | x | = 5 . vertical line x vertical line equals 5 .  Here, the value of x can be 5 or − 5 negative 5  since |5| and | − 5 | absolute value of negative 5 , end absolute value ,  both equal 5.

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