Chapter 12.3, Problem 9MRE

To determine

To calculate: The solution set for open sentence $4\left|4-m\right|=20$ and graph it.

Answer to Problem 9MRE

The solution set is $m=-1\text{ or }m=9$ . The graph is provided below,

Explanation of Solution

Given information:

The open sentence $4\left|4-m\right|=20$ .

Formula used:

For an algebraic expression w and a real number n such that $n>0$ , absolute value inequality is $\left|w\right|=n$ if and only if $w=-n\text{ or }w=n$ .

Calculation:

Consider the open sentence $4\left|4-m\right|=20$ .

Recall that for an algebraic expression w and a real number n such that $n>0$ , absolute value inequality is $\left|w\right|=n$ if and only if $w=-n\text{ or }w=n$ .

Apply it, divide both sides by 4

  $\begin{array}{c}4\left|4-m\right|=20\\ \left|4-m\right|=5\end{array}$

Either $4-m=-5$ or $4-m=5$ .

That is either $4-m=-5$ , simplify it,

  $\begin{array}{c}4-m=-5\\ m=4+5\\ m=9\end{array}$

Or, $4-m=5$ , simplify it,

  $\begin{array}{c}4-m=5\\ m=4-5\\ m=-1\end{array}$

Write it in the set form $\left\{-1,9\right\}$ .

The solution set is two points on real number line that is $m=-1\text{ or }m=9$ .

On the real number mark the points $m=-1\text{ or }m=9$ and darken the points.

Thus, the solution set is $m=-1\text{ or }m=9$ .