Exercise 5 Page 210

We are asked to find and graph the solution set for all possible values of x in the given inequality. |x+2|≥1 To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number that makes the distance between x and -2 greater than or equal to 1 in the positive direction or in the negative direction. x+2 ≥ 1 or x+2≤ -1Let'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 -1 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≥-1 Second Solution Set:& x≤ -3 Combined Solution Set:& x≤ -3 or x≥ -1

Graph

The graph of this inequality includes all values less than or equal to - 3 or greater than or equal to -1. We show this by keeping the endpoints closed.