Exercise 9 Page 161

To solve this inequality, let's begin by isolating the absolute value. Since the absolute value is multiplied by 2, we have to divide both sides of the inequality by 2. 2|x-5|<16 ⇔ |x-5|<8 When we remove the absolute value, we get a compound inequality. - 8< x-5<8If we pull the inequality apart, we need to consider two possible cases. Case1:& x-5>- 8 Case2:& x-5< 8 We can solve each inequality separately.

Case 1

Case 2

Solution Set

Combing the found inequalities, we get a compound inequality. -3integers. From the interval above, let's separate the integers of the solution set. {-2, -1, 0, 1, 2, ..., 12} Let's add these integers together. (-2)+(-1)+...+12=75 Therefore, the correct answer is B.