Chapter 12.3, Problem 8MRE

To determine

To calculate: The solution set for open sentence $\left|9+2k\right|=15$ and graph it.

Answer to Problem 8MRE

The solution set is $\left\{-12,3\right\}$ . The graph is provided below,

Explanation of Solution

Given information:

The open sentence $\left|9+2k\right|=15$ .

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 $\left|9+2k\right|=15$ .

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.

Either $9+2k=-15$ or $9+2k=15$ .

That is either $9+2k=-15$ , simplify it,

  $\begin{array}{c}9+2k=-15\\ 2k=-24\\ k=-12\end{array}$

Or, $9+2k=15$ , simplify it,

  $\begin{array}{c}9+2k=15\\ 2k=15-9\\ 2k=6\\ k=3\end{array}$

Write it in the set form $\left\{-12,3\right\}$ .

The solution set is two points on real number line that is $k=-12\text{ or }k=3$ .

On the real number mark the points $k=-12\text{ or }k=3$ and darken the points.

Thus, the solution set is $\left\{-12,3\right\}$ .