Split the compound inequality into two separate ones and solve them individually.
Solution Set: -3 ≤ a ≤ 2 Graph:
Practice makes perfect
First, let's split the compound inequality into two separate inequalities.
Compound Inequality: -2 ≤ 4-3a& ≤ 13
First Inequality: -2 ≤ 4-3a&
Second Inequality: 4-3a& ≤ 13
Notice that compound inequalities written in this way are equivalent to compound inequalities that involve the word and.
-2 ≤ 4-3a and 4-3a ≤ 13
Now we can solve them separately.
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 flip the inequality sign.
The second inequality is true for numbers greater than or equal to -3.
Notice that a can equal -3 as the inequality sign contains or equal to.
Compound Inequality
The solution set to the compound inequality is the intersection of the solution sets. To help visualize the algebraic expression, we will write a ≥-3 as -3 ≤ a.
First Solution Set: a& ≤ 2
Second Solution Set: - 3≤ a&
Intersecting Solution Set: - 3≤ a& ≤ 2
Finally, we will graph the solution set to the compound inequality on a number line.
