Exercise 26 Page 86

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 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 reverse the inequality sign. The above tells us that all values greater than or equal to $3$ will satisfy the inequality.

Note that the point on $3$ is closed because it is included in the solution set.

Second Inequality

Again, we will solve the inequality by isolating the variable. We found that all values greater than $\text{-}5$ will satisfy the inequality.

Note that the point on $\text{-}5$ is open because it is not included in the solution set.

Compound Inequality

The solution set to the compound inequality is the union of the solution sets. Note that this compound inequality is equivalent to just $m>\text{-}5.$ Finally, we will graph the solution set to the compound inequality.