Solving Compound Inequalities When the word and is used, the solution includes all values that satisfy both inequalities. This is the intersection of the two solution sets. A compound inequality is formed when two inequalities are joined using either the word and or the word or. When the word or is used, the solution includes all values that satisfy one or the other of the inequalities. This is the union of the two solution sets.

Example 1 Solve: Since this is and, we want the intersection. Start by solving each of the inequalities.

We want to find the values of x that are common to both inequalities. A graph will assist in accomplishing this. and

Graph the points on the line that are common to both graphs. The solution is The interval notation answer is

Example 2 Solve: Since this is or, we want the union. Start by solving each of the inequalities.

We want to find the values of x that satisfy one inequality or the other. A graph will assist in accomplishing this. or

Graph the points on the line that are on one graph or the other. The solution is The interval notation answer is