Originally Posted by

**artvandalay11** for all ,x : (-1)x = -x and

come up with the following proof :

**1) (-1)x = (-1)x + 0................................................. .................................................. ..............by using the axiom : for all ,a: a + 0 = a**

**2) (-1)x = (-1)x + ( x + (-x))............................................... ................................................by using the axiom: for all ,a : a + (-a) = 0**

**3) (-1)x = ((-1)x + x) + (-x)................................................ ....................................by using the axiom : for all a,b.c : a + ( b + c) = ( a + b) + c**

That's what I mean, you want (-1)x on one side of the equation and you want to end up with -x on the other side

I caught a mistake that I didn't catch before though in your proof, on line 6 and then line 7, you must first factor the x out, then conclude 1+(-1)=0 and 0x=0, so you skipped a step in there

You may say to yourself, but I did that on the left side, but on line 5 to line 6 you don't make mention that x=1x, but again we're changing all the lefts to (-1)x, so we can ignore that as long as you correct the right side