If we solve each inequality separately, we will find two solution sets. The union of those sets, the set containing values from one set or from the other, is the solution to 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 flip the inequality sign.
We have that all numbers greater than or equal to 5 will satisfy the inequality.
Comparing Solution Sets
We end up with f<- 5 or f≥ 5. In terms of an interval, for the first inequality we have -∞ and - 5 as the endpoints, for the second, 5 and ∞ are the endpoints. When an endpoint is not included, like - 5, we use a parenthesis. When it is included, like 5, we use a bracket. Therefore, we can write the inequality in interval notation.
f<- 5or f≥ 5 ⇔ (-∞,- 5)or [5,∞)
