Chapter 12, Problem 75CLR

To determine

To graph: The solution set of the given inequality.

Answer to Problem 75CLR

The graph is shown in Figure 1.

Explanation of Solution

Given:

The inequality is $3x-y<4$ .

Calculation:

Consider the given inequality $3x-y<4$. Reduce it for y in terms of x , as shown below:

  $\begin{array}{c}3x-y<4\\ 3x-y+y<4+y\left[\text{Adding }y\text{ on both sides}\right]\\ 3x<4+y\\ 3x-4<y\left[\text{Subtracting }4\text{ from both sides}\right]\end{array}$

Create a table for equation $3x-4=y$ to obtain the values of y for different values of x .

x	y
-2	-10
-1	-7
0	-4
1	-1
2	2

Table 1

Plot the coordinates $\left(x,y\right)$ from Table 1 in a graphing utility and join the points with a straight line. Shade the region on the left hand side of the equation.

  

Figure 1