Question 797260: I have trouble with equations involving variables on both sides. This is a simple problem, but no one has shown me HOW to do it when I ask them for help. They do it for me instead.
x + 3 = 3x - 1
Now, I know the next step should look like this:
x + 3 = 3x - 1
+ 1 + 1 =
x + 4 = 3x
I get stuck at this part...
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! You probably should forget everything you
think you know about equations.
(1) Think of the = sign as a balance point, and
there has to be perfect balance of the left
side with the right side.
(2) That means that anything you do to one side, you
have to do the same thing to the other side.
(3) The trick to solving equations is to choose the
right things to do to both sides that will result in
this: ( unknown on one side ) = ( just numbers on the other side )
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If you have unknowns on both sides, what you have to do is
get the unknowns all on the left side ( or all on the right side )
while obeying (1) and (2) above.
----------------------------
You have:
Now you could choose to get rid of the  on the right
side, but it's better to get rid of the  on the left side.
-----------------------------
Subtract from both sides. That keeps the perfect balance.
-----------------
Doing the subtraction, you get
-----------------
You're still not quite there.
You want the unknown all by itself, so
add  to both sides
----------
Doing the addition:
-----------
Still not quite there. Divide both sides by 
----------------
Doing the division:
And you are done
------------------
You did 3 steps: 1 subtraction, 1 addition, 1 division,
but the equation stayed balanced each time.
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Now check your work, Plug  into the original problem
OK
Hope this helps
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