Exercise 33 Page 211

We are asked to find and graph the solution set for all possible values of x in the given inequality. |x|<5 To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number less than 5 away from the midpoint in the positive direction and any number less than 5 away from the midpoint in the negative direction. Absolute Value Inequality:& |x| < 5 Compound Inequality:& -5 < x < 5 This compound inequality means that the distance between x and 0 is greater than -5 and less than 5. x>-5 and x<5 The solution to this type of compound inequality is the overlap of the solution sets. Let's recombine our cases back into one compound inequality. First Solution Set:& x < 5 Second Solution Set:& -5 < x Intersecting Solution Set:& -5 < x < 5

Graph

The graph of this inequality includes all values from -5 to 5, not inclusive. We show this by using open circles on the endpoints.