Chapter 6.5, Problem 8P

Graph each linear inequality.

$\frac{x}{4}<4y-3$

To determine

To graph: the given inequality.

Explanation of Solution

Given information:

The given inequality is

  $\frac{x}{4}<4y-3$

Calculation:

Arrange the inequality as below

  $\begin{array}{l}\frac{x}{4}<4y-3\\ \frac{x}{4}+3<4y\\ \frac{x}{16}+\frac{3}{4}<y\\ y>\frac{x+12}{16}\end{array}$

Consider the line $y=\frac{x+12}{16}$

  $\begin{array}{l}x=0\Rightarrow y=3/4\\ y=0\Rightarrow x=-12\end{array}$

Draw the dotted line passing through the points $(0,3/4)\&(-12,0)$ and then shade the

above the region of the line.

Graph:

The graph of the given inequality is shown below