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Absolute Value
Example 10

Example 10: Absolute Value Equations

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

Problem

Greater solution of x1=6 is ?\text{Greater solution of }|x--1|=6\text{ is }?

1. Recognize Pattern

xh=dx=h±d|x-h|=d\Rightarrow x=h\pm d

2. Apply Method

x9=8x{17,1}|x--9|=8\Rightarrow x\in\left\{-17,-1\right\}

3. Conclude

x=1±6x{7,5}x=-1\pm6\Rightarrow x\in\left\{-7,5\right\}

Final answer

x=1±6x{7,5}x=-1\pm6\Rightarrow x\in\left\{-7,5\right\}