Chapter 3.2, Problem 46WE

To determine

To solve: the given equation for $a$ .

Answer to Problem 46WE

The value of $a$ in the given equation is $a=32\text{or}a=-32$ .

Explanation of Solution

Given information:

Given equation

  $\frac{\left|a\right|}{8}=4$

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

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

Calculation:

Consider the given equation,

  $\frac{\left|a\right|}{8}=4$

Now, solve the equation by multiplying both sides by 8 as shown,

  $\begin{array}{c}\frac{\left|a\right|}{8}\cdot 8=4\cdot 8\\ \left|a\right|=32\\ a=32\text{or}a=-32\end{array}$

Hence, the value of $a$ in the given equation is $a=32\text{or}a=-32$ .