Chapter 2.6, Problem 11E

To determine

To solve: The inequality and to graph the solution

Answer to Problem 11E

Thesolved inequality is $t\le -\frac{2}{3}andt\ge 3$

Explanation of Solution

Given:

  $|6t-7|-8\ge 3$

Calculation:

  $|6t-7|-8\ge 3$

Add both sides by $8$

  $|6t-7|-8+8\ge 3+8$

Write a compound inequality

  $6t-7\le -11or6t-7\ge 11$

Add both sides for both inequalities by $7$

  $6t-7+7\le -11+7or6t-7+7\ge 11+7$

Divide both sides for both inequalities by $6$

  $\frac{6t}{6}\le \frac{-4}{6}or\frac{6t}{6}\ge \frac{18}{6}$

  $t\le -\frac{2}{3}andt\ge 3$

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

Therefore, its graph should have a closed point at $-\frac{2}{3}$ and a shaded line going to the left of $-\frac{2}{3}$ and a closed point at $3$ and a shaded line going to the right of $3$

Conclusion:

Hence, the solved inequality is $t\le -\frac{2}{3}andt\ge 3$