How do you solve and graph #-y+5>=9# or #3y+4< -5#?

1 Answer
Dec 22, 2017

Answer:

See below

Explanation:

First rearrange the inequalities so y is the subject:

#-y+5>=9color(white)(88)# , #color(white)(88)-y >=4# , #color(white)(88)y<=-4#

#3y+4<-5# , #color(white)(88)3y<-9# , #color(white)(88)y<-3#

#color(blue)(y<=-4)#

#color(blue)(y<-3)#

Graph these two lines as #y=-4# and #y=-3#. Remember to use a dashed line for #y=-3#, because this is a less than and not a less than or equal to inequality, so the line will not be an included region.

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We now need to test #y# values in each region A , B and C. These values have to satisfy both inequalities:

Region A:

#y=-1#

#-1<=-4color(white)(88)# False

#-1<-3color(white)(88)# False

A is not an included region.

Region B:

#y=-3.5#

#-3.5<=-4color(white)(88)#False

#-3.5<-3color(white)(8)# True

Region B is not the included region.

Region C:

#y=-5#

#-5<=-4color(white)(88)#True

#-5<-3color(white)(88)#True

Region C satisfies both, so region C is the included region.

enter image source here