Chapter 5.5, Problem 26E

To determine

To Solve: the equation by graphing and check the solution.

Answer to Problem 26E

  $x=1andx=4$

Explanation of Solution

Given:

  $\left|x+2\right|=\left|-3x+6\right|$

Separate the equation into two possible cases

  $\begin{array}{l}x+2=-3x+6\hfill \\ x+2=-\left(-3x+6\right)\hfill \end{array}$

For the first case:

  $\begin{array}{l}x+2=-3x+6\hfill \\ y=x+2\hfill \\ y=-3x+6\hfill \end{array}$

The graph intersects at $\left(1,3\right)$ .

  

For the second case:

  $\begin{array}{l}y=x+2\hfill \\ y=-\left(3x+6\right)\hfill \\ y=3x-6\hfill \end{array}$

The graph of intersection is (4, 6)

  

Hence the solutionis $x=1andx=4.$

Check:

  $\left|x+2\right|=\left|-3x+6\right|$

For $x=1$ ,

  $\begin{array}{l}\left|1+2\right|=\left|-3\left(1\right)+6\right|\hfill \\ \left|3\right|=\left|-3+6\right|\hfill \\ \left|3\right|=\left|3\right|\hfill \\ 3=3\hfill \end{array}$

Hence true.

For $x=4$

  $\begin{array}{l}\left|4+2\right|=\left|-3\left(4\right)+6\right|\hfill \\ \left|6\right|=\left|-12+6\right| \hfill \\ \left|6\right|=\left|-6\right|\hfill \\ 6=6\hfill \end{array}$

Hence true.

Conclusion:$x=1andx=4$