How do you graph the inequality #3-x>0# and #y+x< -6#?

1 Answer
Somebody N.
Jan 22, 2018

See below.

Explanation:

First we write the inequalities as linear equations, and the graph these. Remember to use a dashed line, as these are not equal to inequalities, so the line itself will not be an included region.

#3-x>0#

#3-x=0# , #x=3color(white)(88888888888)# First equation.

#y+x<-6#

#y+x=-6# , #y=-x-6color(white)(88)# Second equation.

We now graph these:

enter image source here

With graph plotted, we can see that there are four possible regions.

A , B , C and D

The required region has to satisfy both inequalities, so we test a set of coordinates in each region. We can save some work by realising that if a coordinate in a region fails for the first inequality we test, then the region can't be the required region and it is not necessary to test the other inequality as well.

Region A

Coordinates: #(-2 ,2)#

#color(blue)(3-x>0)#

#3-(-2)>0color(white)(88)# , #5>2color(white)(88888888)# TRUE

#color(blue)(y+x<-6)#

#2+(-2)<-6color(white)(88)# ,#0<-6color(white)(888)# FALSE

Region A is not the required region.

Region B

Coordinates: #(2 ,2)#

#color(blue)(3-x>0)#

#3-(2)>0color(white)(88)# , #1>0color(white)(888888888)# TRUE

#color(blue)(y+x<-6)#

#2+2<-6color(white)(88)# , #4<-6color(white)(888)color(white)(88)# FALSE

Region B is not the required region.

Region C

Coordinates: #(-2 , -6)#

#color(blue)(3-x>0)#

#3-(-2)>0color(white)(88)# , #5>0color(white)(888888888888888)# TRUE

#color(blue)(y+x<-6)#

#(-6)+(-2)<-6color(white)(88)# , #-8<-6color(white)(8888)# TRUE

Region C is a required region.

We do not need to test region D. As can be seen from the graph above if C is an included region and is to the left of the line #x=3#, then to the right of this line is an excluded region.

Shade the required region C

enter image source here

Related questions
See all questions in Linear Inequalities in Two Variables
Impact of this question
1782 views around the world
You can reuse this answer
Creative Commons License