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Absolute Value
Example 12

Example 12: Absolute Value Equations

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

Problem

Greater solution of x9=3 is ?\text{Greater solution of }|x-9|=3\text{ is }?

1. Recognize Pattern

xh=dx=h±d|x-h|=d\Rightarrow x=h\pm d

2. Apply Method

x10=2x{12,8}|x--10|=2\Rightarrow x\in\left\{-12,-8\right\}

3. Conclude

x=9±3x{6,12}x=9\pm3\Rightarrow x\in\left\{6,12\right\}

Final answer

x=9±3x{6,12}x=9\pm3\Rightarrow x\in\left\{6,12\right\}