Since the word between the inequalities is and, we are looking for where the solution sets intersect.
Solution Set: 12≤ p≤16 Graph:
Practice makes perfect
To solve the compound inequality, we will solve each of the inequalities separately and then graph them together. The intersection of these solution sets is the solution set for the compound inequality.
First Inequality
Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when we divide or multiply by a negative number, we must reverse the inequality sign.
The second inequality is satisfied for all values of p that are less than or equal to 16.
Note that the point on 16 is closed because it is included in the solution set.
Compound Inequality
The solution to the compound inequality is the intersection of the solution sets.
First Solution Set: 12≤ p&
Second Solution Set: p&≤ 16
Intersecting Solution Set: 12≤ p& ≤ 16
Finally, we will graph the solution set to the compound inequality on a number line.
