Example

Find the solution set for the compound inequality. Write the solution set in interval notation and graph it on a number line.

Solution

This compound inequality is an "OR" inequality. The solution set will be the union of the solution sets for each individual inequality. So, let's solve each individual inequality.

or

or

The solution set for the first inequality is $(-\infty,0]$.

Now we solve the second inequality.

or

or

The solution set for the second inequality is $(4,\infty)$.

The solution of the compound inequality is the union of the two intervals:

The graph of the solution set is