Since the word between the inequalities is and, we are looking for where the solution sets intersect.
Solution Set: - 4≤ k<7.5 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 you divide or multiply by a negative number, you must reverse the inequality sign.
The above tells us that all values greater than or equal to 4 will satisfy the second inequality.
Note that the point on 4 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. To help visualize the algebraic expression, we will write k≥ 4 as 4≤ k.
First Solution Set:&& k& < 7.5
Second Solution Set:&& - 4 ≤ k&
Intersecting Solution Set:&& - 4 ≤ k& < 7.5
Finally, we will graph the solution set to the compound inequality on a number line.
