Chapter 2, Problem 27CR

To determine

To solve and graph: the given inequality

Answer to Problem 27CR

The required result is $f\ge 3\text{ and }f\le 9$

  $b<-12$ or $b\ge -4$

  

Explanation of Solution

Given:

  $5|b+8|-7>13$

Calculation:

  $5|b+8|-7>13$

  $5|b+8|-7+7>13+7$

Add both side by 7

  $\frac{5|b+8|}{5}>\frac{20}{5}$

Divide both sides by 5

  $b+8<-4$ or $b+8>4$

Write a compound inequality

  $b+8-8<-4-8$ or $b+8-8>4-8$

Subtract both sides for

both inequalities by 8

  $b<-12$ or $b\ge -4$

Since the inequalities are joined by "or", take the union of the inequalities as its solution set.

Therefore, its graph should have an open point at -12 and a shaded line going to the left of -12 and a closed point at -4 and a shaded line going to the right of -4, as in:

  

Conclusion:

The required result is $f\ge 3\text{ and }f\le 9$

  $b<-12$ or $b\ge -4$