Chapter 2.3, Problem 28E

To determine

To explain:

The correct equation for the following inequalities equation or its graphing solution:

Answer to Problem 28E

The correct inequality equation is $-4y\le -32$ and the number line graph of the solution $y\ge 8$ is:

Explanation of Solution

Given information:

From the image:

The main inequality equation is $-4y\le -32$ . On solving:

  $\begin{array}{l}-4y\le -32\\ \frac{-4}{-4}y\le \frac{-32}{-4}\\ y\le 8\end{array}$

Here need to reverse the inequality sign is an error of this problem. So, the correct method is:

The given inequality equation is:

  $-4y\le -32$

Reverse the inequality sign by multiplying $-1$ on both sides:

  $\begin{array}{l}-4y\le -32\\ \left(-4\right)\left(-1\right)y\ge \left(-32\right)\left(-1\right)\\ 4y\ge 32\end{array}$

Now, divide by $4$ for both sides of above equation:

  $\begin{array}{l}4y\ge 32\\ \frac{4}{4}y\ge \frac{32}{4}\\ y\ge 8\end{array}$

So, the solution of $-4y\le -32$ is $y\ge 8$ . Now the number line graph of the solution $y\ge 8$ is: