Check whether the equations are identities. Write the patterns got form each,on taking x = 1, 2, 3, 4, 5 and x = –1, –2, –3, –4, –5.

–x + (x + 1) = 1

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.