Chapter 1.8, Problem 14E

To determine

To graph: the given inequality.

Answer to Problem 14E

  

Explanation of Solution

Given information:

  $-4\le x-y\le 5$

Calculation:

This inequality has two parts as shown below.

  $\begin{array}{l}-4\le x-y\\ x-y\le 5\end{array}$

Rearrange both the inequalities in terms of y as follows:

  $\begin{array}{l}y\le x+4\\ x-5\le y\end{array}$

Create a table by plugging the different values x in the line equation $y=x+4$ to evaluate the value for y.

$x$	$y$
-5	-1
-3	1
-1	3
0	4
1	5
3	7
5	9

Since the inequality has greater than or equal to sign $(\le )$ , solid line will be used to graph a line $y=x+4$ .

Put the test points $\left(-6,1\right)$ and $\left(0,0\right)$ in the inequality and check the true test point as follows:

Test point $\left(x,y\right)$	Inequality, $y\le x+4$	True/False test point
$\left(0,0\right)$	$\begin{array}{l}0\le 0+4\\ 0\le 4\end{array}$	True
$\left(-6,1\right)$	$\begin{array}{l}1\le -6+4\\ 1\le -2\end{array}$	False

Create a table by plugging the different values x in the line equation $x-5=y$ to evaluate the value for y.

$x$	$y$
-1	-6
0	-5
1	-4
3	-3
5	0
7	2
9	4

Since the inequality has greater than or equal to sign $(\le )$ , solid line will be used to graph a line $x-5=y$ .

Put the test points $\left(7,1\right)$ and $\left(0,0\right)$ in the inequality and check the true test point as follows:

Test point $\left(x,y\right)$	Inequality, $x-5\le y$	True/False test point
$\left(0,0\right)$	$\begin{array}{l}0-5\le 0\\ -5\le 0\end{array}$	True
$\left(7,1\right)$	$\begin{array}{l}7-5\le 1\\ 2\le 1\end{array}$	False

The graph for the given inequality is shown below.