Exercise 27 Page 86

To solve the compound inequality, we will solve each of the inequalities separately and then graph them together. The intersection of these solution sets is the solution set for 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. This above tells us that all values greater than or equal to $\text{-}5$ will satisfy the inequality.

Note that the point on $\text{-}5$ is closed because it is included in the solution set.

Second Inequality

Again, we will solve the inequality by isolating the variable. The second inequality is satisfied for all values of $y$ that are greater than $7.$

Note that the point on $7$ is open because it is not included in the solution set.

Compound Inequality

The solution to the compound inequality is the intersection of the solution sets. Note that the intersection of the solution sets is just $y>7.$ Finally, we will graph the solution set to the compound inequality.