Since the word between the inequalities is or, we are looking for the union of the solution sets to the individual inequalities.
Solution: b<- 1 or b>2 Graph:
Practice makes perfect
We are given a compound inequality. 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 reverse the inequality sign.
The second inequality is satisfied for all values of b greater than 2. Again, the inequality is strict meaning b cannot be equal to 2.
Comparing Solution Sets
Now we must compare our solution sets. From the first inequality, we know that the solution set consists of all numbers to the left of - 1 on the number line, without including - 1 itself.
From the second inequality, we know the solution set includes all values to the right of 2, but not including 2.
The union of these solution sets is two intervals b<- 1 or b>2.
