Take as x different positive numbers, negative numbers and zero, and compute x + 1, x – 1, 1 – x. Check whether the equations below hold for all numbers.

(1 + x) + (1 – x) = 2

Let take as positive numbers as: 1,2,3,4

Negative numbers: - 1,-2,-3,-4 and 0

For positive number:

(x + 1) = 1 + 1, 2 + 1 ,3 + 1 ,4 + 1

= 2,3,4,5

(x-1) = 1-1, 2-1 ,3-1 ,4-1

= 0, 1, 2, 3

(1-x) = 1-1, 1-2, 1-3, 1-4

= 0, -1, -2, -3

(i) (1 + x) + (1-x) = 2

Let’s check for x = 1

L.H.S = (1 + 1) + (1-1)

= 2 + 0

= 2

= R.H.S

Hence, it works for x = 2

Let’s check for x = 3

L.H.S = (1 + 3) + (1-3)

= 4 – 2

= 2

= R.H.S

Hence, it works for x = 3

Similarly, we can check for other values too. It will follow.