Question

Multiplication Property of Negative One
Prove that -1x X= -X
a.−1×x+x=−1×x+1×x b.=(−1+1)(x) c.=0×x d. =0 e. =−x+x f.∴−1×x+x=−x+x g.∴−1×x=−x
could anyone help me w/ the reasons for this??? like mult. prop. of = or sth...

Answer 1

just say its common sense.

Answer 2

Start from the idea that
x=x

Subtract x from both sides x-x=0

(by additive inverse property)

subtract x from both sides again
(x-x)-x= -x

This gives
0-x=-x

(again by additive inverse prop)

factor out a -1

-1(0+x)=-x

(by distributive law)

collapse equation
-1(x)=-x

(by zero as neutral additive element)