Chapter 1.4, Problem 30PPS

To determine

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

Answer to Problem 30PPS

The value of $w$ in the given equation is $w=\frac{1}{5}$ .

Explanation of Solution

Given information:

Given equation

  $8\left|5w-1\right|=0$

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,

  $8\left|5w-1\right|=0$

Now, solve the equation as shown,

  $\begin{array}{c}8\left|5w-1\right|=0\\ \frac{8\left|5w-1\right|}{8}=\frac{0}{8}\\ \left|5w-1\right|=0\\ 5w-1=0\\ 5w-1+1=0+1\\ 5w=1\\ w=\frac{1}{5}\end{array}$

Now, check the result by back substitution.

  $\begin{array}{c}8\left|5w-1\right|=0\\ 8\left|5\left(\frac{1}{5}\right)-1\right|=0\\ 8\left|1-1\right|=0\\ 8\left|0\right|=0\\ 0=0\end{array}$

Which is true.

Hence, the value of $w$ in the given equation is $w=\frac{1}{5}$ .