Chapter 1.8, Problem 7CFU

To determine

To graph: the given inequality.

Answer to Problem 7CFU

  

Explanation of Solution

Given information:

  $y<\left|x+3\right|$

Calculation:

Create a table by plugging the different values x in the line equation $\left(y=\left|x+3\right|\right)$ to evaluate the value for y.

$x$	$y$
-5	2
-4	1
-3	0
-2	1
-1	2
0	3
1	4
2	5
3	6
4	7
5	8

Since the inequality has less than sign (<), dotted line will be used to graph a line $y=\left|x+3\right|$ .

Put the test points $\left(3,3\right)$ and $\left(-3,3\right)$ in the inequality and check the true test point as follows:

Test point $\left(x,y\right)$	Inequality, $y<\left|x+3\right|$	True/False test point
$\left(3,3\right)$	$\begin{array}{l}3<\left|3+3\right|\\ 3<\left|6\right|\\ 3<6\end{array}$	True
$\left(-3,3\right)$	$\begin{array}{l}3<\left|-3+3\right|\\ 3<\left|0\right|\\ 3<0\end{array}$	False

The graph for the given inequality is shown below.