Question 698582: 2x-3. X+2
______ = ______
5. 6
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 
The road to the solution of an equation may have several steps.
In each step you change the equation into an equivalent equation, that has exactly the same solution(s), and is easier to solve.
As for driving (or even walking) you have to look at the road far ahead to make sure that with each step you are going in the right direction.
If you look at the ground just in front of you, you may zigzag, walk in the wrong direction, or even go around in circles.
I'll show you what steps I would take, and you can decide if each step makes the equation easier to solve.
At the end, I will give you a general tip (note) about how I plan my steps.
STEP 1 - Get rid of denominators (usually a good first step).
If you multiply both sides of the equal sign times the same (non-zero) number,
you get an equivalent equation, that has exactly the same solution(s).
Multiplying times 5 would get rid of the denominator on the left side.
Multiplying times 6 would get rid of the denominator on the right side.
We can do both at the same time by multiplying times 
Most people would write it as  , but I see it more clearly if I write it as  .
 -->  -->  --> 
You probably have no problem solving , but I'll show how I would solve it.
STEP 2
If you add the same expression to both sides of an equation,
you get an equivalent equation, that has exactly the same solution(s).
I would add  to both sides.
 -->  --> 
NOTES:
Your teacher may think that you should do that in two steps (done in any order),
adding  to both sides in one step, and
subtracting  from both sides in the other step.
Going from  to  sound as natural as 12 apples minus 5 apples = 7 apples,
but your teacher may say that you have to show that you are "taking out the common factor x",
or that you are applying the distributive property.
Then you would have to write
-->  --> .
Whatever your teacher wants, it is wise to humor him or her.
STEP 3
If you divide both sides of the equal sign by the same (non-zero) number,
you get an equivalent equation, that has exactly the same solution(s).
-->  --> 
A GENERAL NOTE:
When solving simple (beginning algebra) equations,
I try to "undo" all the "processing" done to the x in the expressions involved.
That "processing" was done in a certain order, according to the "order of operations" rules.
When "undoing" it, I must do it in reverse order.
It just like taking off my shoes before taking off my socks when I undress,
because I put my socks on before putting my shoes on when I dressed.
Example:
In  , the variable  is first multiplied by  ,
and after that, 2 is added.
My first step must undo the adding of  :
-->  --> 
The next step is undoing the times multiplication:
-->  --> 
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