Help with equation

[anniev2]

Here is a solution to an equation however I would have solved it differently and incorrectly for that matter.

Correct:
–x – 1 = 2x – 1
0 = 3x
0 = x

Why does my method not yield the same result:
–x – 1 = 2x – 1
–x = 2x – 1 + 1
–x = 2x

From here I would think that both sides should be divided by x or by -1 but that is obviously incorrect.

[DanaJ]

Why does my method not yield the same result:
–x – 1 = 2x – 1
–x = 2x – 1 + 1
–x = 2x

From here I would think that both sides should be divided by x or by -1 but that is obviously incorrect.

Well, so you get that:
-x = 2x - add x to each side to get:
0 = 3x.

So your solution is correct, but you shouldn't divide both sides by x. If you do that, you get that:
-1 = 2 - which is obviously FALSE.

[zephir21]

In fact it does match

-x = 2x
0 = 2x + x
0 = 3x .....

So you got it right

[anniev2]

I see where I went wrong...

I thought that whenver a variable is alone on the side of an equation that it should be divided. However now I understand that if the variable was being added or subtracted to begin with then it should be added or subtracted for elimination.

Is this correct?