Chapter 5.4, Problem 33E

To determine

To solve: $\left|2x+6\right|=\left|x\right|$

Answer to Problem 33E

The solution is $x=-6,-2$

Explanation of Solution

Given information: $\left|2x+6\right|=\left|x\right|$

Calculation:

  $\left|2x+6\right|=\left|x\right|$

The equation can be written as,

  $\begin{array}{l}2x+6=x\\ \Rightarrow 2x-x=-6\\ \Rightarrow x=-6\end{array}$ or $\begin{array}{l}2x+6=-x\\ \Rightarrow 2x+x=-6\\ \Rightarrow 3x=-6\\ \Rightarrow x=-\frac{6}{3}\\ \Rightarrow x=-2\end{array}$

Thus, the solution is $x=-6,-2$