2.2.3 Solving Absolute-Value Equations and Inequalities (continued)
Example 2 Solving Absolute-Value Equations
Recall that the absolute value of a number x , written | x |, is the distance from x to 0 on a number line. Because absolute value represents distance without regard to direction, the absolute value of any real number is nonnegative. Absolute-value equations can be represented by compound statements. • For all real numbers x and all positive real numbers a , if | x | = a , then x = a or x = − a . Use the following steps to solve an absolute-value equation. 1. Isolate the absolute-value expression, if necessary. 2. Rewrite the absolute-value equation as an “or” compound statement. 3. Solve each of the two equations in the compound statement.
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