Chapter 3, Problem 20GR

Solution

To graph: The inequality $y>\left|x-6\right|+2$ .

Given information:

  $y>\left|x-6\right|+2$

Calculation:

First make the inequality sign to equality.

  $y=\left|x-6\right|+2$

Make the table of $x$ and $y$ by taking some random values of $x$ and calculating the corresponding values of $y$ .

The value of $x$ are:

  $x=0,6,12$

Substitute $x=0$ into the equation $y=\left|x-6\right|+2$ and solve for $y$ .

  $\begin{array}{c}y=\left|0-6\right|+2\\ y=6+2\\ y=8\end{array}$

Similarly, calculate $y$ for $x=6$ and $x=12$ .

The table of $x$ and $y$ ,

  $\begin{array}{cccc}x& 0& 6& 12\\ y& 8& 0& 8\end{array}$

Take a test point $\left(0,0\right)$ and check the position of point.

  $\begin{array}{c}y>\left|x-6\right|+2\\ 0>\left|0-6\right|+2\\ 0>8\end{array}$

It is false. The shaded region away from the point $\left(0,0\right)$ . The line should be dotted because here inequality without equal sign.

Plot the points on graph and connect the points and shade the region.