Since the word between the inequalities is or, we are looking for the union of the solution sets to the individual inequalities.
Solution: All real numbers Graph:
Practice makes perfect
To solve the compound inequality, we have to solve each of the inequalities separately. Since the word between the individual inequalities is or, the solution set for the compound inequality is the union of the individual solutions.
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.
All possible values of n that are greater than or equal to -1 will satisfy the first inequality.
Note that the point on - 1 is closed because it is included in the solution set.
Second Inequality
In this case, we can isolate n by dividing by - 5 on both sides of the inequality. Remember that we will have to flip the inequality sign, since we divide by a negative number.
The second inequality is satisfied by all values of n less than - 1.
Note that the point on - 1 is open because it is not included in the solution set.
Combining Our Solutions
The solution to the compound inequality is the union of the solution sets.
First Solution Set:& n≥- 1
Second Solution Set:& n<- 1
Combined Solution Set:& n≥- 1 or n<- 1
Finally, we will graph the solution set to the compound inequality.
