Question

How do I solve this?
3x + 1 = (1/3)x + 9

Answer 1

I'm having trouble finding the first step.

Answer 2

Try to bring the variables on one side and constants on the other side

Answer 3

How do I do that? Where do I start?

Answer 4

Basically combine like terms
Can you identify like terms ?

Answer 5

I can identify them. How should I move the like terms when they are on different sides of the = sign? That's what I'm a little confused about

Answer 6

When we want to cancel things out or get them on one side we do the opposite operation.
3x + 1 = (1/3)x + 9

All numbers here are posititve so we will be subtracting
I'll get you started off :)
We want to isolate x so we will start by putting the x's with the x's and constants with constants
Let's start by subtracting 1 from both sides
\[\huge~\rm~\bf~3x + 1-1 = (1/3)x + 9-1\]
What equation do we have once we subtract 1 from both sides?

Answer 7

3x = (1/3)x + 8

Answer 8

Good any ideas on what to do next?

Answer 9

Should I subtract 3x from both sides?

Answer 10

Not quite...remember that we want constants on one side and variables on another side

Answer 11

How about 1/3x?

Answer 12

What would we do with the 1/3?

Answer 13

3x - (1/3)x = (1/3)x + 8 - (1/3)x
(2 2/3)x = 8

Does this look alright?

Answer 14

Yes however let's leave it as an improper fraction it'll make things alot more easier ;)
So we have
\[\huge~\rm~\bf~ \frac{ 8 }{ 3 }x=8\]
Any ideas on how we can isolate the x?

Answer 15

OK. Hmmm. This?
(8/3)x/(8/3) = 8/(8/3)
x = 3

Answer 16

Perfect! :)

Answer 17

Now I understand! Thanks!:)

Answer 18

You're welcome ^.~