What is the answer to this 2x-3y<6 ?

Question

I cannot get the answer and I am supposed to graph the inequality.

Answer 1

2x-3y<6
-3y<-2x+6
y>2/3x-2

Answer 2

Your first step is to treat this like an equation, and put it into slope-intercept form, even though it's not an equal sign.

2x - 3y < 6

Move -2x to the right hand side, to get

-3y < -2x + 6

Now, divide both sides by -3. One thing to note is that for inequalities, whenever you divide or multiply by a negative number, the sign changes.

y > (2/3) x - 2

At this point, what you would do is graph the line y = (2/3) x - 2. Since it is strictly greater than (as opposed to greater than or equal to), you would have to graph the line as light dashes.

From here, you're going to do one of two things: shade everything above the line, or everything below the line.

How do you know which to shade? The simple answer to that is to test ANY point, and see if the inequality y > (2/3) x - 2 holds true. Let's test (0,0). Plugging in x = 0 and y = 0, we get

0 > (2/3) (0) - 2
0 > 0 - 2
0 > -2

This is a FALSE statement. Therefore, what you would shade is the side of the line y = (2/3) x - 2 that does NOT lie on the same side that (0,0) does.

Answer 3

i have not done this math in a long time, but i believe it to be 2x-3y = -1y then 1y<6 is -6y dont know about the graphing though, and i could be TOTALLY off, just in case im kind of close i'll TRY to help you.. dont just use my answer though lol
-kakez

Answer 4

The region in question is the subspace of the cartesian plane below the line y = (2/3)x - 2.

QED

Answer 5

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