Exercise 32 Page 211

We are asked to find and graph the solution set for all possible values of x in the given inequality. |x|≥ 3To 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 0 greater than or equal to 3 in the positive direction or in the negative direction. x ≥ 3 or x≤ - 3 In this case, our absolute value expression is only the variable x, so our compound inequality does not need any more simplifying.

Graph

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