Since we are given a compound inequality, we can split it into two separate inequalities to solve it.
Compound Inequality: - 9< 3m& +6≤ 18
First Inequality: - 9< 3m& +6
Second Inequality: 3m&+6≤ 18
We can solve each of these inequalities separately. 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.
We have two solution sets, m>- 5 and m≤ 4. We can combine these into a compound inequality.
- 5 < m≤ 4
In terms of an interval, we have - 5 and 4 as the endpoints. When an endpoint is not included, like - 5, we use a parenthesis. When it is included, like 4, we use a bracket. Therefore, we can write the inequality in interval notation as shown below.
(- 5,4]
