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Absolute Value
Example 5

Example 5: Absolute Value Equations

Step-by-step worked example for this lesson track.

Problem

Greater solution of x3=5 is ?\text{Greater solution of }|x--3|=5\text{ is }?

1. Recognize Pattern

xh=dx=h±d|x-h|=d\Rightarrow x=h\pm d

2. Apply Method

x7=2x{5,9}|x-7|=2\Rightarrow x\in\left\{5,9\right\}

3. Conclude

x=3±5x{8,2}x=-3\pm5\Rightarrow x\in\left\{-8,2\right\}

Final answer

x=3±5x{8,2}x=-3\pm5\Rightarrow x\in\left\{-8,2\right\}