Chapter 1.5, Problem 64S

To determine

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

Answer to Problem 64S

The value of $x$ in the given equation is $x=9\text{or}x=-3$ .

Explanation of Solution

Given information:

Given equation

  $\left|3x-9\right|=18$

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,

  $\left|3x-9\right|=18$

Now, solve the equation as shown,

  $\begin{array}{c}\left|3x-9\right|=18\\ 3x-9=18\text{or}3x-9=-18\\ 3x-9+9=18+9\text{or}3x-9+9=-18+9\\ 3x=27\text{or}3x=-9\\ x=9\text{or}x=-3\end{array}$

Now, check the result by back substitution.

  $\begin{array}{c}\left|3x-9\right|=18\\ \left|3\left(9\right)-9\right|=18\\ \left|27-9\right|=18\\ \left|18\right|=18\\ 18=18\end{array}$

And

  $\begin{array}{c}\left|3x-9\right|=18\\ \left|3\left(-3\right)-9\right|=18\\ \left|-9-9\right|=18\\ \left|-18\right|=18\\ 18=18\end{array}$

Which is true.

Hence, the value of $x$ in the given equation is $x=9\text{or}x=-3$ .