Question

Solve for x in terms of a.
ax + 2a = 4x + 7a

Answer 1

Any ideas?

Answer 2

No my teacher helped me but he accidentally told me how to get a not x. So now I'm confused

Answer 3

He showed you how to solve for a?

Answer 4

Yeah.

Answer 5

use the same idea to solve for x

Answer 6

He said that but I don't know how.

Answer 7

what grade?

Answer 8

9th but I haven't taken algebra since 7th

Answer 9

OK, the whole idea behind solving equations is to use the idea of "balance." By that I mean what ever you do to one side of $$\Huge ax + 2a = 4x + 7a $$ you do the same to the other, to keep the equation "balanced."

Answer 10

Yeah...I understand that part.

Answer 11

So here we want to solve for x, that is to express x in terms of the other variable.

Answer 12

Like this $$\Huge x=?$$

Answer 13

Are you clear about the objective here?

Answer 14

That I'm supposed to get x?

Answer 15

I have the answer to the problem I just don't know how to get to there

Answer 16

In math getting there is ALL the fun :-)

Answer 17

Well I don't think it's fun because I don't get it.

Answer 18

What we are asked to do is to "get x" alone, right?

Answer 19

Yep

Answer 20

So lets look at the equation as a whole: $$ax + 2a = 4x + 7a$$ where is x?

Answer 21

On both sides

Answer 22

Good, but we want to get it alone so what should we do?

Answer 23

Subtract?

Answer 24

Yes, subtraction would move the x where?

Answer 25

Let's subtract 4x from both sides.

Answer 26

I don't know. I thought I was supposed to subtract 2a

Answer 27

OK subtract 2a from both sides.

Answer 28

See the fun, we can do whatever we want :-)

Answer 29

I guess. So now I have ax= 4x+5a

Answer 30

Excellent. Now what?

Answer 31

Remember the objective!!!

Answer 32

I guess subtract 4x but I thought they have to be common. 4x doesn't have a in it

Answer 33

It does NOT have to be common, only the idea of balance must be maintained.

Answer 34

Wait so would it be 4x-ax=5a

Answer 35

ax= 4x+5a
ax - 4x = 4x + 5a -4x

Answer 36

Subtract 4x from both sides, right?

Answer 37

Yeah but the 4x on the right side gets cancelled out

Answer 38

That is WHY we did it that way, right?

Answer 39

In math always keep your objective in mind.

Answer 40

Yeah so it is 4x-ax=5a

Answer 41

Beyond this point I have no idea how to do this to get x= 5a/a-4

Answer 42

You got this far ax= 4x+5a, now subtract 4x from both sides, please.

Answer 43

I thought i did