Answer :

–x – (x + 1) + (x + 2) + (x + 3) = 4

We will calulate LHS in every case and compare it with RHS


Taking x = 1,


= -1-(1 + 1) + (1 + 2) + (1 + 3)


= -1-2 + 3 + 4


= 4


Taking x = 2,


= -2-(2 + 1) + (2 + 2) + (2 + 3)


= -2-3 + 4 + 5


= 4


Taking x = 3,


= -3-(3 + 1) + (3 + 2) + (3 + 3)


= -3-4 + 5 + 6


= 4


Taking x = 4,


= -4-(4 + 1) + (4 + 2) + (4 + 3)


= -4-5 + 6 + 7


= 4


Taking x = 5,


= -5-(5 + 1) + (5 + 2) + (5 + 3)


= -5-6 + 7 + 8


= 4


Taking x = -1,


= 1-(-1 + 1) + (-1 + 2) + (-1 + 3)


= 1 + 0 + 1 + 2


= 4


Taking x = -2,


= 2-(-2 + 1) + (-2 + 2) + (-2 + 3)


= 2 + 1 + 0 + 1


= 4


Taking x = -3,


= 3-(-3 + 1) + (-3 + 2) + (-3 + 3)


= 3 + 2-1 + 0


= 4


Taking x = -4,


= 4-(-4 + 1) + (-4 + 2) + (-4 + 3)


= 4 + 3-2-1


= 4


Taking x = -5,


= 5-(-5 + 1) + (-5 + 2) + (-5 + 3)


= 5 + 4-3-2


= 4


As in each case in LHS = 4 so, LHS = RHS


Hence, above equation is an identity.


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