Solving Absolute Value Equations

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In this section, we learn how to solve absolute value equations. First, we need to remember that the absolute value of a number is the distance between that number and zero on the number line. We will also revisit the concept of an additive inverse or opposite. Recall that opposites have the same absolute value. So 3 and -3 are opposites and |3| = |-3|. In both cases, the absolute value is 3. We will use this information to help us understand how to set up and solve an absolute value equation. Suppose we say that |x| = 7. This means we could replace x with 7 or -7, since |7| = 7 and |-7| = 7. This leads to a simple method to solve an absolute value equation. We isolate the absolute value part and set up a compound equation with "or". As an example: |2x + 3| = 5 would lead to: 2x + 3 = 5 or 2x + 3 = -5. This is due to the absolute value operation. We could replace x with a value that leads to |-5| = 5 or |5| = 5. Either, gives us a true statement.
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