Question #4c249

Given:

#5x-3y>6#

Subtract 5x from both sides of the inequality:

#-3y> -5x +6#

When we divide both sides by negative number (in this case -3), we must change the direction of the inequality:

#y< (-5)/-3x +6/-3#

Simplify:

#y< 5/3x -2#

This matches selection B.

#5x-3y>6#

All of these inequalities have y as the subject. So lets manipulate our given inequality, almost like it is an equation, to make y the subject.

#5x-3y>6#
#-3y>6-5x#
#-y>2-5/3x#

Now, this part is where we need to remember we are dealing with an inequality, not an equation. With an inequality, when dividing by a negative number, you need to flip the sign. I'll show why later on.
Keeping this in mind:

#y<-2+5/3x#
#y<5/3x-2#

Now, to show why you can't divide by -1 normally

#4=4# (I hope you'll agree)
#4+1=4+1#
#(4+1)/7=(4+1)/7#
#12((4+1)/7)=12((4+1)/7)#
#-12((4+1)/7)=-12((4+1)/7)#

Everything we do with an equation is fine.

Now, for an inequality:

#3<4#
#3+1<4+1#
#(3+1)/7<(4+1)/7#
#12((3+1)/7)<12((4+1)/7)#
So far, so good. Now dividing by a negative.
#-12((3+1)/7)<-12((4+1)/7)#
Oops, this is wrong. Evaluating both sides we get:
#-48/7<-60/7#
Which is wrong. Therefore, flipping the sign:
#-48/7> -60/7# is correct, and all is good.