Chapter 1.5, Problem 36PPS

To determine

To solve: the given inequality and graph the solution on number line.

Answer to Problem 36PPS

The solution is given by $z\le 3$ .

Explanation of Solution

Given information:

Given inequality

  $\frac{9z-4}{5}\le \frac{7z+2}{4}$

Calculation:

Consider the given inequality,

  $\frac{9z-4}{5}\le \frac{7z+2}{4}$

Now, solve the inequality as shown,

  $\begin{array}{c}\frac{9z-4}{5}\le \frac{7z+2}{4}\\ \frac{9z-4}{5}\cdot 5\le \frac{7z+2}{4}\cdot 4\\ 9z-4\le 7z+2\\ 9z-4+4-7z\le 7z+2+4-7z\\ 2z\le 6\\ \frac{2z}{2}\le \frac{6}{2}\\ z\le 3\end{array}$

Now, graph the inequality as shown:

The closed ball suggests that the solution region is included the point $3$ .

Lesser than sign indicates the region is left side to the point $3$ on number line.

Hence, the solution of the inequality is $z\le 3$ .