Chapter 5.5, Problem 21E

To determine

The solution of the equation.

Answer to Problem 21E

  $x=-2$ is the solution.

  $x=1$ is the solution.

Explanation of Solution

Given:

The given equation is:

  $\left|x-4\right|=\left|3x\right|$

Calculation:

The equations can be written as:

  $\begin{array}{l}x-4=3x\mathrm{............}\left(1\right)\\ x-4=-3x\mathrm{..........}\left(2\right)\end{array}$

Step 1: Write the system of linear equations:

  $\begin{array}{l}\text{Equation 1:}\\ x-4=3x\\ \downarrow \downarrow \\ y=x-4y=3x\\ \\ \text{Equation 2:}\\ x-4=-3x\\ \downarrow \downarrow \\ y=x-4y=-3x\end{array}$

Step 2: Make input-output table:

For system 1:

  

Draw the graphs:

  

Both the lines are intersecting at $x=-2$ . Hence, $x=-2$ 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 $x=-2$ and $x=1$ ,

  $\begin{array}{l}\left|x-4\right|=\left|3x\right|\left|x-4\right|=\left|3x\right|\\ \left|-2-4\right|=\left|3\left(-2\right)\right|\left|1-4\right|=\left|3\left(1\right)\right|\\ \left|-6\right|=\left|-6\right|\left|-3\right|=\left|3\right|\\ 6=63=3\end{array}$