Write each inequality as a compound inequality first.
See solution.
Practice makes perfect
We are given two absolute value inequalities, let's look at them one at a time.
First inequality
First, let's rewrite the absolute value inequality as a compound inequality. |x|<5 will become an "and" compound inequality because we need the solution sets where the values of x are less than 5 units away from 0 :
|x|<5 ⇒ -5
We can graph these intervals on a number line. The interval -5
Because it is an "and" compound inequality, both conditions must be met and the overlap is the solution set. It is the "intersection" of these two intervals, the interval where the points belong to both sets.
Second inequality
First, let's rewrite the absolute value inequality as a compound inequality. |x|>5 will become an "or" compound inequality because we need the solution sets where the values of x are greater than 5 units away from 0 :
|x|>5 ⇒ -55.
We can graph these intervals on a number line. The interval -5>x is represented with a blue line and x>5 with a red line.
Because it is an "or" compound inequality, the solution set includes all values that are contained in either set. It is the "union" of these two intervals.
