Chapter 3.3, Problem 22PPE

To determine

To graph: The solution of the inequality $-4w\le 20$ and check the solution.

Explanation of Solution

Given information:

The inequality $-4w\le 20$ .

Graph:

The graph of the solution of the given inequality can be drawn by solving the inequality as,

To solve an inequality, simply add, subtract, multiply or divide the numbers on both sides till variable is left alone on one side.

So, in the given inequality, divide both sides by $-4$ and dividing by a negative number will change the sign of inequality as,

  $\begin{array}{c}-4w\le 20\\ \frac{-4w}{-4}\ge \frac{20}{-4}\\ w\ge -5\end{array}$

The solution of the inequality $-4w\le 20$ is $w\ge -5$ which is plotted on the graph as,

Interpretation:

The solution of the inequality represents that the inequality will hold true for any number greater than $-5$ . For any number less than or equal to $-5$ , will make the inequality false.

To check, substitute $w=-4$ in $-4w\le 20$ ,

  $\begin{array}{c}-4w\le 20\\ -4\left(-4\right)\le 20\\ 16<20\end{array}$

Since, the inequality holds true for the number greater than $-5$ , thus, $w\ge -5$ is the solution of the given inequality.