Chapter 8.2, Problem 79SR

To determine

To solve: the given inequality and check the solution.

Answer to Problem 79SR

The solution is given by $z\ge -48$ .

Explanation of Solution

Given information:

Given inequality

  $\frac{z}{4}+7\ge -5$

Calculation:

Consider the given inequality,

  $\frac{z}{4}+7\ge -5$

Now, solve the inequality as shown,

  $\begin{array}{c}\frac{z}{4}+7\ge -5\\ \frac{z}{4}+7-7\ge -5-7\\ \frac{z}{4}\ge -12\\ z\ge -48\end{array}$

Now, check the solution by taking a valueequal to $-48$ as shown:

  $\begin{array}{c}\frac{z}{4}+7=-5\\ \frac{-48}{4}+7=-5\\ -12+7=-5\\ -5=-5\end{array}$

Now, check the solution by taking a value greater than $-48$ as shown:

  $\begin{array}{c}\frac{z}{4}+7>-5\\ \frac{-44}{4}+7>-5\\ -11+7>-5\\ -4>-5\end{array}$

Which is true.

Hence, the solution of the inequalityis $z\ge -48$ .