Chapter 3.4, Problem 31PPE

To determine

To solve: The inequality $-2\left(6+s\right)\ge -15-2s$ . If the inequality has no solution, write no solution. If the solution are all real numbers, write all real numbers.

Answer to Problem 31PPE

The inequality $12\ge -15$ is never true and so the inequality $-2\left(6+s\right)\ge -15-2s$ has no solutions.

Explanation of Solution

Given information: The inequality is $-2\left(6+s\right)\ge -15-2s$ .

Calculation:

Use distributive property to simplify the inequality $-2\left(6+s\right)\ge -15-2s$ as follows.

  $12-2s\ge -15-2s$

Add 2s on both sides and simplify further.

  $\begin{array}{l}12-2s+2s\ge -15-2s+2s\\ 12\ge -15\end{array}$

Since the inequality $12\ge -15$ is never true, the inequality $-2\left(6+s\right)\ge -15-2s$ has no solutions.