Chapter 1.5, Problem 20PPS

To determine

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

Answer to Problem 20PPS

The solution is given by $y>\frac{8}{3}$ .

Explanation of Solution

Given information:

Given inequality

  $\frac{3y-4}{0.2}-8>12$

Calculation:

Consider the given inequality,

  $\frac{3y-4}{0.2}-8>12$

Now, solve the inequality as shown,

  $\begin{array}{c}\frac{3y-4}{0.2}-8>12\\ \frac{3y-4}{0.2}-8+8>12+8\\ \frac{3y-4}{0.2}>20\\ \frac{3y-4}{0.2}\cdot 0.2>20\cdot 0.2\\ 3y-4>4\\ 3y-4+4>4+4\\ 3y>8\\ y>\frac{8}{3}\\ y>2.667\end{array}$

Now, graph the inequality as shown:

The open ball suggests that the solution region is not included the point $\frac{8}{3}$ .

Greater than sign indicates the region is right side to the point $\frac{8}{3}$ on number line.

Hence, the solution of the inequality is $y>\frac{8}{3}$ .