Chapter 1.5, Problem 54SR

To determine

To solve: the given equation for $x$ . Check the result.

Answer to Problem 54SR

The value of $x$ in the given equation is $x=-7\text{or}x=17$ .

Explanation of Solution

Given information:

Given equation

  $\left|x-5\right|=12$

Concept used:

Absolute value of a function a is given by

  $\left|a\right|=\{\begin{array}{l}aa>0\\ -aa<0\\ 0a=0\end{array}$ \

And

  $\begin{array}{l}\left|-a\right|=a\\ \left|a\right|=a\end{array}$

More over

  $\begin{array}{l}\left|x+a\right|=b\\ \Rightarrow x+a=b\text{or}x+a=-b\end{array}$

Calculation:

Consider the given equation,

  $\left|x-5\right|=12$

Now, solve the equation as shown,

  $\begin{array}{c}\left|x-5\right|=12\\ x-5=-12\text{or}x-5=12\\ x-5+5=-12+5\text{or}x-5+5=12+5\\ x=-7\text{or}x=17\end{array}$

Now, check the result by back substitution.

  $\begin{array}{c}\left|x-5\right|=12\\ \left|-7-5\right|=12\\ \left|-12\right|=12\\ 12=12\end{array}$

And

  $\begin{array}{c}\left|x-5\right|=12\\ \left|17-5\right|=12\\ \left|12\right|=12\\ 12=12\end{array}$

Which is true.

Hence, the value of $x$ in the given equation is $x=-7\text{or}x=17$ .