Example 10: Absolute Value Equations

Absolute Value

Example 10

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

Problem

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

1. Recognize Pattern

|x-h|=d\Rightarrow x=h\pm d

2. Apply Method

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

3. Conclude

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

Final answer

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