Chapter 2.6, Problem 15E

To determine

To solve: The inequality and to graph the solution

Answer to Problem 15E

Thesolved inequality is $w\ge -4andw\le -\frac{4}{3}$

Explanation of Solution

Given:

  $2|3w+8|-13\le -5$

Calculation:

  $2|3w+8|-13\le -5$

Add both sides for both inequalities by $13$

  $2|3w+8|-13+13\le -5+13$

Divide both sides by $2$

  $\frac{2|3w+8|}{2}\le \frac{8}{2}$

Write a compound inequality

  $3w+8\ge -4and3w+8\le 4$

Subtract both sides of both inequalities by $8$

  $3w+8-8\ge -4-8and3w+8-8\le 4-8$

  $\frac{3w}{3}\ge \frac{-12}{3}and\frac{3w}{3}\le \frac{-4}{3}$

Simplify

  $w\ge -4andw\le -\frac{4}{3}$

Since the inequalities are joined by “and”, take the intersection of the inequalities as its solution set.

Therefore, its graph should have a closed point at $-4$ and a shaded line going to the right until the closed point at $-\frac{4}{3}$ as in:

  

Conclusion:

Hence, the solved inequality is $w\ge -4andw\le -\frac{4}{3}$