Question

8 – 4(x – y) = 2x + 6 How to solve this? Please don't give me the answer, want to know how to solve it.

Answer 1

Begin by distributing the term -4(x-y).

Answer 2

8 - 4(x - y) = 2x + 6
8 - 4x - 4y = 2x + 6

Answer 3

like that?

Answer 4

Almost!

Answer 5

Look at your second term in that distribution: -4y.

What is (-4)*(-y)?

Answer 6

ohhh, so it'd be... +(positive) 4y?

Answer 7

Correct! So we now have

8 - 4x + 4y = 2x + 6.

The next step is to combine like terms. Do you know how to do that?

Answer 8

I think so: 8 - 4x - 2x + 4y = 6?

Answer 9

Well done! Do you agree that -4x-2x=-6x?

Answer 10

Yes, but how did we get to -6x? What about the 8? (Math is not my best subject)

Answer 11

We're just simplifying right now:

8 - 4x - 2x + 4y = 6
8 - 6x + 4y = 6

Answer 12

By the way, are we trying to solve for y?

Answer 13

oohh, I thought that when you put the equation, that that was the final equation. I'm supposed to just write the equation in the simplest form, but I want to also know how to solve it, so I have back up in case I get a question like that.

Answer 14

Okay. :)

Now that we have

8 - 6x + 4y = 6,

our next step would be to combine the remaining two "like" terms 8 and 6. Could you do that?

Answer 15

8 - 6x + 4y - 8 = 6 - 8
So, it would end up as, -6x + 4y = -2 correct?

Answer 16

That's right. :)

Now, the expression can't be simplified any further, but you could rewrite it as much as you want.

For example, you could divide both sides by two to obtain

-3x+2y=-1.

Answer 17

Ohh, my answers are
A.
6x – 4y = –2

B.
6x – 4y = 2

C.
4x – 6y = 2

D.
6x + 4y = 2

how do I turn the six into positive?

Answer 18

Ah, I see. :)

Well, we ended up with

-6x + 4y = -2.

If we multiply both sides by -1, what would we end up with?

Answer 19

6x + 4y x -1 = -2 x -1
so that would be, 6x + 4y = 2!

Answer 20

Very close!

Answer 21

Or do I have to multiply the 4y too?

Answer 22

What happens to the + 4y term?

Answer 23

Yep!

Answer 24

that means it's 6x - 4y = 2?

Answer 25

There you go. :)

Answer 26

Yes! Thanks a bunch, math was never my favorite subjects :P Thanks again

Answer 27

You're most welcome!