Chapter 5.5, Problem 23E

To determine

The solution of the equation.

Answer to Problem 23E

  $x=3$ is the solution.

  $x=-1$ is the solution.

Explanation of Solution

Given:

The given equation is:

  $\left|2x\right|=\left|x+3\right|$

Calculation:

The equations can be written as:

  $\begin{array}{l}2x=x+\mathrm{3............}\left(1\right)\\ 2x=-\left(x+3\right)\mathrm{..........}\left(2\right)\end{array}$

Step 1: Write the system of linear equations:

  $\begin{array}{l}\text{Equation 1:}\\ 2x=x+3\\ \downarrow \downarrow \\ y=2xy=x+3\\ \\ \text{Equation 2:}\\ 2x=-\left(x+3\right)\\ \downarrow \downarrow \\ y=2xy=-\left(x+3\right)\end{array}$

Step 2: Make input-output table:

For system 1:

  

Draw the graphs:

  

Both the lines are intersecting at $x=3$ . Hence, $x=3$ 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 $x=3$ and $x=-1$ ,

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