Question

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

Answer 1

See below.

Explanation:

First graph the line `y=1/x+1`. This is a `<=` 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

`( -1 ,4 )`

`4<=1/(-1)+1`

`4<=0color(white)(888)` FALSE

Region A is an excluded region.

Region B

`(1 , 6 )`

`6<= 1/(1)+1`

`6<= 2color(white)(888)` FALSE

Region B is an excluded region.
**
Region C**

`( -1 ,-6 )`

`-6<= 1/(-1)+1`

`-6<= 0color(white)(888)` TRUE

**Region C is an included region.
**

Region D

`( 1 , -6 )`

`-6<=1/(1)+1`

`-6<=2color(white)(888)` TRUE

Region D is an included region.

Shade included regions C and D