Chapter 1.5, Problem 21PPS

To determine

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

Answer to Problem 21PPS

The solution is given by $z<3$ .

Explanation of Solution

Given information:

Given inequality

  $\frac{9z+5}{4}+18<26$

Calculation:

Consider the given inequality,

  $\frac{9z+5}{4}+18<26$

Now, solve the inequality as shown,

  $\begin{array}{c}\frac{9z+5}{4}+18<26\\ \frac{9z+5}{4}+18-18<26-18\\ \frac{9z+5}{4}<8\\ \frac{9z+5}{4}\cdot 4<8\cdot 4\\ 9z+5<32\\ 9z+5-5<32-5\\ 9z<27\\ \frac{9z}{9}<\frac{27}{9}\\ z<3\end{array}$

Now, graph the inequality as shown:

The open ball suggests that the solution region is not 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 $z<3$ .