Example 7: Absolute Value Equations

Absolute Value

Example 7

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

Problem

\text{Greater solution of }|x--6|=5\text{ is }?

1. Recognize Pattern

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

2. Apply Method

|x--6|=5\Rightarrow x\in\left\{-11,-1\right\}

3. Conclude

x=-6\pm5\Rightarrow x\in\left\{-11,-1\right\}

Final answer

x=-6\pm5\Rightarrow x\in\left\{-11,-1\right\}