Chapter 2.6, Problem 13E

To determine

To solve: The inequality and to graph the solution

Answer to Problem 13E

Thesolved inequality is $m>20orm<8$

Explanation of Solution

Given:

  $3|14-m|>18$

Calculation:

  $3|14-m|>18$

Divide both sides by $3$

  $\frac{3|14-m|}{3}>\frac{18}{3}$

Write a compound inequality

  $14-m<-6or14-m>6$

Subtract both sides for both inequalities by $14$

  $14-14-m<-6-14or14-14-m>6-14$

Divide both sides for both inequalities by $-1$

  $\frac{-m}{-1}<\frac{-20}{-1}or\frac{-m}{-1}\ge \frac{-8}{-1}$

Reverse inequality symbol

  $m>20orm<8$

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 $8$ and a shaded line going to the left of $8$ and an open point at $20$ and a shaded line going to the right of $20$

  

Conclusion:

Hence, the solved inequality is $m>20orm<8$ and the graph is drawn