Question

can someone please help me answer this question? I will fan and give a medal!!
Question~
write the following inequalities in y = mx + b form.
–3x –4y > 12

Answer 1

it just wants you to get y by itself. so add 3x to both sides and then divide both sides by -4

Answer 2

@notshh so to add 3x to both sides it will look like this?
(-3)–3x –4y > 12(-3) ?

Answer 3

adding 3x (not -3x) to both sides would give you
-4y >12 + 3x

then from there, divide -4 from both sides. what do you get?

Answer 4

change the inequality also,because when we multiply or divide by a negative quantity sign of inequality changes.

Answer 5

^ ye

Answer 6

@notshh
I am very sorry for not replying sooner!! I'm so sorry!
If you don't mind helping me still I would really like your help.. Please...
~~~ Can you check my steps when I divide by -4?
Divide both sides by -4
(-4) -4y>12+3x(-4)
(-4)/-4=1
3/(-4)= 0.75
=
1y>12+0.75x

Answer 7

–3x –4y > 12 is to be solved for 4y, and then for y alone.

You may find it easier to multiply this whole inequality by (-1), remembering to reverse the direction of the > symbol.

You should get 3x+4y<12.

Subtract 3x from both sides. Show your work.

Divide both sides of that result by 4. This is the inequality you wanted, in the form

y<mx+b.

Answer 8

I'm not really following your work. D:
But the final answer you got looks as if you divided by a positive 4 instead of -4.

so from here
–4y > 3x + 12
after dividing by -4, the inequality sign (>) will be flipped to <, and the numbers to the right of the sign will change to negative.

Answer 9

oh ok, could you try to show me what it looks like when dividing? Like the steps you do? Because I'm a little confused on what it should look like...

Answer 10

just divide each term by -4

-4y ÷ -4 = ?
3x ÷ -4 = ?
12 ÷ -4 = ?

Answer 11

-4y ÷ -4 = 1
3x ÷ -4 = -0.75
12 ÷ -4 = -3
Then what?

Answer 12

You may choose which approach you prefer:
1) multiply the given inequality by (-1) and also reverse the direction of the > symbol, or
2) don't bother to change the given inequality by (-1).

Since you and notshh have started out by following the latter approach,

Add 3x to both sides of the equation to move the term -3x to the right side:

–3x –4y > 12
+3x = 3x
--------------
-4y>12+3x

Next, divide each of these 3 terms by -4 to isolate y, and change the direction of the > sign.

-4y > 12 + 3x
----- --- ---
-4 -4 -4

Change the direction of the inequality sign now.

Next, simplify. Abby, your turn!

Answer 13

\[\frac{ -4y }{ -4 }=?\]

Answer 14

\[\frac{ 12 }{ -4 }=?\]

Answer 15

\[\frac{ 3x }{-4 }=?\]

Answer 16

now that you know all the values, you can write the inequality. don't forget to flip the inequality sign since you divided by a negative.

Answer 17

@mathmale

–3x –4y > 12
Multiplying the inequality above by -1 on both sides gives
3x + 4y < -12

(It's -12, not 12)

Answer 18

@mathmale so all I have to do is simplify the fractions ?

Answer 19

That's right. But watch the signs carefully.

Answer 20

Step 1: Multiply by '-' (negative symbols) on both sides of the equation

Why?
It makes the equation have positive signs as ('-'x'-' is '+')

Looks like after multiplying by negative sign:
3x+4y<-12

Observe the inequality symbol
( changed from > to <)

Why does it change?

Assume: 5>4
If I multiply both sides by -1 and keep the symbol as same, it is an error
-5>-4

As we all know, -5 is lesser than -4.
Hence the above is incorrect, so we flip the inequality
Got it?

Step 2: Subtract 3x on both sides


We are concentrating on the form y=mx+b
So, we see that y is singled out on LHS

So, lets keep 'y' on one side of the '=' symbol.
Oops, but we've got 4y. So, keep '4y' on LHS.

Subtract 3x on both sides of the equation as 3x is added on both sides.

Looks like after subtracting:
4y<-12-3x

Step 3:
Now, our aim is to get only 'y'. So, we divide by 4 on both sides as it is multiplied with 'y'.

Now, the answer looks like after dividing by 4 on both sides:
y<(-12-3x)/4

I hope you get it, I 'll respond if you have any more doubts regarding this if I have time.

Answer 21

-4/-4=1
12/-4= -3
3/-4= -3/4
@mathmale

Answer 22

That's right

Answer 23

-4/-4=1 is actually -4y/(-4) = ? (Can't drop the variable.)

Your other two divisions turned out fine.

Answer 24

so it would be 1y?

Answer 25

Now put all three terms into the appropriate places in one inequality.

Either 1y, or simply y.

Answer 26

Abby: Note the appropriate cautionary message I received from mathstudent55:

"–3x –4y > 12
Multiplying the inequality above by -1 on both sides gives
3x + 4y < -12

(It's -12, not 12)"

He's right. Take this into account as y ou write your final answer (inequality).

Answer 27

All you'll need to do (following his point) is to change one sign in your inequality.

Answer 28

oh ok, Thank you all so much!!! I understand it now! Thank y'all again!

Answer 29

My pleasure. Thanks, mathstudent55, praavi and notshh.