Exercise 10 Page 97

We are asked to find and graph the solution set for all possible values of q in the given inequality. |2q+8|>4 To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number with a distance greater than 4 away from the midpoint in the positive direction or a distance greater than 4 away from the midpoint in the negative direction. 2q+8 > 4 or 2q+8< - 4Let's isolate q in both of these cases before graphing the solution set.

First Inequality

This inequality tells us that all values greater than -2 will satisfy the inequality.

Second Inquality

This inequality tells us that all values less than - 6 will satisfy the inequality.

Compound Inequality

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& q>-2 Second Solution Set:& q<-6 Combined Solution Set:& q<-6 or q>-2

Graph

The graph of this inequality includes all values less than - 6 or greater than - 2. We show this with open circles on the endpoints.