Chapter 12.3, Problem 2MRE

To determine

To calculate: The solution set for open sentence $2\left|y+7\right|=10$ and graph it.

Answer to Problem 2MRE

The solution set is $y=-12\text{ or }y=-2$ . The graph is provided below,

Explanation of Solution

Given information:

The open sentence $2\left|y+7\right|=10$ .

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 $2\left|y+7\right|=10$ .

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 2

  $\begin{array}{c}2\left|y+7\right|=10\\ \left|y+7\right|=5\end{array}$

Either $y+7=-5$ or $y+7=5$ .

That is either $y=-12$ or $y=-2$ .

Write it in the set form $\left\{-12,-2\right\}$ .

The solution set is two points on real number line that is $y=-12\text{ or }y=-2$ .

On the real number mark the points $y=-12\text{ or }y=-2$ and darken the points.

Thus, the solution set is $y=-12\text{ or }y=-2$ .