Question

Question #4c249

Answer 1

Selection B. `y<5/3x-2`

Explanation:

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.

Answer 2

B
`y<5/3x-2`

Explanation:

`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.