# How do solve 1/x+1>=0 graphically?

Jan 3, 2018

See below.

#### Explanation:

First graph the line $y = \frac{1}{x} + 1$. This is a $\le$ inequality so use a solid line, because the line is an included region.

With graph plotted, there will be four possible regions: A, B , C , D

We have to test coordinates in each region to identify which are included regions and which are excluded regions:

Region A

$\left(- 1 , 4\right)$

$4 \le \frac{1}{- 1} + 1$

$4 \le 0 \textcolor{w h i t e}{888}$ FALSE

Region A is an excluded region.

Region B

$\left(1 , 6\right)$

$6 \le \frac{1}{1} + 1$

$6 \le 2 \textcolor{w h i t e}{888}$ FALSE

Region B is an excluded region.

Region C

$\left(- 1 , - 6\right)$

$- 6 \le \frac{1}{- 1} + 1$

$- 6 \le 0 \textcolor{w h i t e}{888}$ TRUE

Region C is an included region.

Region D

$\left(1 , - 6\right)$

$- 6 \le \frac{1}{1} + 1$

$- 6 \le 2 \textcolor{w h i t e}{888}$ TRUE

Region D is an included region.

Shade included regions C and D