Chapter 5.5, Problem 22E

To determine

The solution of the equation.

Answer to Problem 22E

  $x=-5$ is the solution.

  $x=-1$ is the solution.

Explanation of Solution

Given:

The given equation is:

  $\left|2x+4\right|=\left|x-1\right|$

Calculation:

The equations can be written as:

  $\begin{array}{l}2x+4=x-\mathrm{1............}\left(1\right)\\ 2x+4=-\left(x-1\right)\mathrm{..........}\left(2\right)\end{array}$

Step 1: Write the system of linear equations:

  $\begin{array}{l}\text{Equation 1:}\\ 2x+4=x-1\\ \downarrow \downarrow \\ y=2x+4y=x-1\\ \\ \text{Equation 2:}\\ 2x+4=-\left(x-1\right)\\ \downarrow \downarrow \\ y=2x+4y=-\left(x-1\right)\end{array}$

Step 2: Make input-output table:

For system 1:

  

Draw the graphs:

  

Both the lines are intersecting at $x=-5$ . Hence, $x=-5$ is the solution.

For system 2:

  

Draw the graphs:

  

Both the lines are intersecting at $x=-1$ . Hence, $x=-1$ is the solution.

Check: Put $x=-5$ and $x=-1$ ,

  $\begin{array}{l}\left|2x+4\right|=\left|x-1\right|\\ \left|2\left(-5\right)+4\right|=\left|-5-1\right|\\ \left|-10+4\right|=\left|-6\right|\\ 6=6\\ \\ \left|2x+4\right|=\left|x-1\right|\\ \left|2\left(-1\right)+4\right|=\left|-1-1\right|\\ \left|2\right|=\left|-2\right|\\ 2=2\end{array}$