When are numbers negative?

I did two problems just now and both had positive answers, while I mistakenly got negative answers.

The first, $\displaystyle 16x^2 - 16x^2 - 3x$

I thought it would equal 3x, since x - x = 0 and 0 - 3x = -3x

The other, $\displaystyle \frac{6x^2}{x^2-1}=6$ While I got the opposite answer.

Can anyone explain *why* these answers aren't positive?

Re: When are numbers negative?

Just multiply -3x by minus one.

For the second problem:

$\displaystyle \frac {6x^2}{x^2 - 1} = 6 $

$\displaystyle \frac {x^2 - 1}{6x^2} = \frac {1}{6} $

$\displaystyle (6)(x^2 - 1) = (1)(6x^2) $

$\displaystyle 6x^2 - 6 = 6x^2 $

$\displaystyle (6x^2 -6x^2) -6 = 0$

$\displaystyle 0 - 6 = 0 $

$\displaystyle -6 = 0 $

$\displaystyle (-6)(-1) = (0)(-1) $

$\displaystyle 6 $

You could have just multiplied out $\displaystyle x^2 - 1 $ instead.

Re: When are numbers negative?

Quote:

Originally Posted by

**Nervous** I did two problems just now and both had positive answers, while I mistakenly got negative answers.

The first, $\displaystyle 16x^2 - 16x^2 - 3x$

I thought it would equal 3x, since x - x = 0 and 0 - 3x = -3x

The other, $\displaystyle \frac{6x^2}{x^2-1}=6$ While I got the opposite answer.

Can anyone explain *why* these answers aren't positive?

what does "the first" mean ? I don't see an equation ...

fyi, the second equation has no solution for x.