Before we can match the inequalities with their corresponding graphs, we should solve them for x. It is not easy to visualize the graphs with the fractions.
Option
Inequality
Isolated x
a
x/m<-1
x<- m
b
x/m>1
x>m
c
x/m<1
x
d
-x/m<1
x>- m
Now we can easily match the graphs with the inequalities.
Graph A
Graph A shows a positive value for m with the shading to the right. This would correspond with the inequality x>m, option b.
Graph B
Graph B shows a positive value for m with the shading to the left. This would correspond with the inequality x
Graph C
Graph C shows a negative value for m with the shading to the left. This would correspond with the inequality x<- m, option a.
Graph D
Graph D shows a negative value for m with the shading to the right. This would correspond with the inequality x>- m, option d.
