Prove that (-1)a = -a using the 5 properties of real numbers, cancellation, zero, and equality.?

Question

The properties should be used are:
1) Distributive Property
2) Additive Inverse Property
3) Multiplicative Identity Property
4) Multiplication Property Of Zero
5) Cancellation Property Of Addition

Please answer this question because the answers given in my last question was not correct.
The proving should start with the equation:
(-1)a = -a
And should end also in the equation:
(-1)a = -a
Please answer on or before Sunday, August 26, 2007 on any time zone.

The properties should be used are:
1) Distributive Property
2) Additive Inverse Property
3) Multiplicative Identity Property
4) Multiplication Property Of Zero
5) Cancellation Property Of Addition

You should use ALL properties indicated above.

Please answer this question because the answers given in my last question was not correct.
The proving should START with the equation:
(-1)a = -a
And should END also in the equation:
(-1)a = -a
Please answer on or before Sunday, August 26, 2007 on any time zone.

Answer 1

(-1)a + a = (-1)a + (1)a ;Multiplicative Identity Property
=(-1 + 1)a ;Distributive Property
= 0 ;Multiplication Property Of Zero

This means (-1)a is an additive inverse if a ;Cancellation Property Of Addition

Since the additive inverse is unique (-1)a = -a

By the way you can't start a proof by writing what you want to prove first!! (In this case you can't write (-1)a = -a as the first line of your proof. It comes last!!)

Answer 2

Here the equation 5x + 7 = 2 ==> 5x = 2-7 ==> 5x = -5 ==> x = -1 ... OK! To confirm just put x=-1 in the equation and get.... 5(-1) + 7 = -5+7 = 2 OK! confirmed.

Answer 3

When dy/dx said "additive identity," he meant to say "additive inverse."

Answer 4

yes because in algebraic expression it is automatic