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

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Answer 1 · 2018-01-03T09:52:50

See below.

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

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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

enter image source here