Answer :

Let’s take as x = 1,2,3,4,5 (positive numbers)

And as x = -1,-2,-3,-4,-5 (negative numbers)


(i) –x + (x + 1) = 1


We will calculate LHS in every case and compare it with RHS taking x = 1, = -1 + (1 + 1) = -1 + 2


= 1


Taking x = 2, = -2 + (2 + 1) = -2 + 3


= 1


taking x = 3,


= -3 + (3 + 1)


= -3 + 4 = 1


taking x = 4,


= -4 + (4 + 1)


= -4 + 5 = 1


taking x = 5,


= -5 + (5 + 1)


= -5 + 6 = 1


now taking x as negative numbers Taking x = -1, = -(-1) + (-1 + 1)


= 1 – 1 + 1 = 1


Taking x = -2, = -(-2) + (-2 + 1)


= 2 + 1 -2 = 1


Taking x = -3, = -(-3) + (-3 + 1)


= 3 -3 + 1 = 1


Taking x = -4, = -(-4) + (-4 + 1)


= 4 -4 + 1 = 1


Taking x = -5, = -(-5) + (-5 + 1)


= 5 – 5 + 1 = 1


As in each case LHS = 1 so, LHS = RHS


Hence, above equation is an identity.


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