How do you decide which number to subtract from both sides of an equation

Thanks Badinage,

This is a very good question - one that is deserving of a proper answer.

I will try to give you some idea anyway

 

I will work through this example

3x+6 = -4+9

*  First you need to simplify each side independently. 

3x+6 cannot be simplified but -4+9=5    So the equation becomes

3x+6=5

Now you say - I want the lots of x by themself so what do I want to get rid of

ok I want to get rid of the +6   the opposite of +6 is minus 6  BUT

if I minus 6  from one side I have to minus 6  from the other side too.  The equation must stay balanced!

3x+6=5

     -6   -6

3x     = -1

NOW I want the x by itself so what do I need to get rid of.

 I need to get rid of the 3.  How do I do that?   Well between the 3 and the x is an invisable multiply sign

3*x=-1

The opposite of mult is divide and a divide is the same as a fraction line. So I have to divide both sides by 3

 

$$\\\frac{\not{3}*x}{\not{3}}=\frac{-1}{3}\\\\
x=\frac{-1}{3}$$

 

I hope that helps :)

The equation tells you. You subtract a term to make it vanish from a particular side of the equation, usually as part of your manouvering to isolate a variable by itself. In the process of making it disappear from one side, you inevitably cause it to appear on the other side.

 

 

Just make sure you are even-handed, what you do to one side must also be done to the other. You can divide everything on one side by some number, as long as you divide all on the other side by that same number. (Just make sure you don't try to do any division by zero!)