Split the compound inequality into two separate ones and solve them individually.
Solution: - 21≤ q≤ 33 Graph:
Practice makes perfect
We are given the following compound inequality.
- 3≤ 6-q/9≤ 3
Sometimes, it can be helpful to write a compound inequality as two individual inequalities. This lets us solve each one separately.
- 3≤6-q/9 and 6-q/9≤ 3Now we can solve them separately and later compare their solution sets.
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 all values greater than or equal to - 21.
Combining Solution Sets
Finally, we can combine the obtained solution sets. The first inequality, q≤ 33, describes all values less than or equal to 33. We can represent this by using a closed circle at 33 and shading the values to the left.
The second inequality, q≥ - 21, describes all values greater than - 21, including - 21. For this, we will use a closed circle again, this time at - 21 and shade the values to the right.
The intersection of these solution sets, - 21≤ q≤ 33, describes the solutions of the compound inequality.
