Exercise 32 Page 46

We are asked to find and graph the solution set for all possible values of x in the given inequality. |x-5|≥ 8 To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number greater than or equal to 8 away from the midpoint in the positive direction or any number greater than or equal to 8 away from the midpoint in the negative direction. x-5 ≥ 8 or x-5 ≤ - 8Let's isolate x in both of these cases before graphing the solution set.

Case 1

This inequality tells us that all values greater than or equal to 13 will satisfy the inequality.

Case 2

This inequality tells us that all values less than or equal to -3 will satisfy the inequality.

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& x ≥13 Second Solution Set:& x ≤ -3 Combined Solution Set:& x ≤ -3 or x ≥ 13

Graph

The graph of this inequality includes all values less than or equal to -3 or greater than or equal to 13. We show this by keeping the endpoints closed.