Question

Verify that -(-x) =x for :

1. X=11/15

2. X=-13/17

Answer 1

Case 1
-(-11/5) = 11/15

-(-) = +

So, 11/15 = 11/15

Therefore case 1 is proved

Case 2

-(-(-13/17) = -13/17

-(+) = -

-13/17 = -13/17

Therefore case 2 is proved

(i) x = 11/15 The additive inverse of x = 11/15 is -x = -11/15 as 11/15 + (-11/15) = 0 The same equality 11/15 + (-11/15) = 0 , shows that the additive inverse of -11/15 is 11/15 or -(-11/15) = 11/15 i.e. -(-x) = x

(ii) x = -13/17 The additive inverse of x = -13/17 is -x = 13/17 as (-13/17) + 13/17 = 0 The same equality 13/17 + (-13/17) = 0 , shows that the additive inverse of 13/17 is -13/17 or -(13/17) = -13/17 i.e. -(-x) = x