Chapter 5, Problem 1RE

To determine

To graph: The given inequality $x>2y-3$.

Explanation of Solution

Given:

The inequality is $x>2y-3$

Procedure used:

To graph the linear inequality use the following steps.

Step1: First graph $Ax+By=C$ , if the equality is not included in the original statement then the line will be  dashed line, or as a solid line if the equality is included.

Step2: Choose a test point anywhere in the plane not on the line [the origin $(0,0)$ usually requires the least computation], and substitute the coordinates into the inequality.

Step3: Does the test point satisfy the original inequality. If so, shade the half plane that contain the test point. if not, shade the opposite half plane.

Graph:

Steps involved to graph of inequality $x>2y-3$.

Step1: First draw the graph of the equation $x=2y-3$.

Step 2: Choose the test point above or below the line. Let’s take $(0,0)$ , now the inequality is

$\begin{array}{l}x>2y-3\\ 0>2(0)-3\\ 0>-3\end{array}$

The statement is true. So $(0,0)$ is the solution set of the inequality $x>2y-3$.

Step 3: Hence the graph of the solution set of the inequality $x>2y-3$ is shaded region which will include the origin.

It is observed that the solution set contain origin and the solution set is the shaded region excluding boundary line.