Algebra mistake?

Question

x = -x
x/-x = -x/-x
-1 = 1

Obviously this isn't true. What's gone wrong?

Answer 1

x=-x, only when x=0 and your have divided both sides with -x or '-0' which is equal to '0'. Division by zero is not allowed. This has gone wrong.

Answer 2

x=0

Answer 3

x = - x
x + x = 0
2x = 0
x = 0

therefore, its correct that this algebra is wrong. what went wrong is "-1 = 1".

since 0 = -0 (<<< same thing)

Answer 4

x = -x >>Reorder the terms
x + x = 0 >>Bring all unknown x to the left and there are nothing in the right so we considered as 0.
2x = 0
x = 0 / 2
x = 0

Answer 5

What has gone wrong? See below :
x = -- x => 2x = 0 => x = 0. OK.
then x / --x and --x / --x are meaningless as
we can't divide any number by zero.

Answer 6

if x equals negative x, the new problem should read like this:

-x/--x equals --x/--x

remember your rule that (-)*(-) = +

--x=x so now you have x=x which is true...

-x/x equals x/x

therefore the 1st part of the equasion (-x/x) would be a negative number, and the 2nd equasion (x/x) would be the positive......

answer looks right to me if your x=1.

Answer 7

You went wrong because you divided....the main purpose of -x in the equation is to subtract...so by bringing it over you would have had to use the opposite operation i.e addition....

Answer 8

There is no such mathematical thorem like that.
I think, it is all about proving. And see the result, left side is not =to right side.
You were absolutely right!

Answer 9

x = -x
Add x to each side:
2x = 0
Divide by 2:
x = 0.

You cannot therefore divide by x or by -x and expect valid results.

Answer 10

you have not resolved your equation

x=-x
2x=0
x=0 and this is true -0=+0

x=-x is true ONLY for x=0