i. -x + (x + 1) = 1
If x = 1, -x + (x + 1)
= -1 + (1 + 1) = -1 + 2 = 1
If x = 2, -x + (x + 1)
= -2 + (2 + 1) = -2 + 3 = 1
If x = 3, -x + (x + 1)
= -3 + (3 + 1) = -3 + 4 = 1
If x = 4 -x + (x + 1)
= 4 + (4 + 1) = -4 + 5 = 1
If x = 5, -x + (x + 1)
= -5 + (5 + 1) = -5 + 6 = 1
If x = -1, -x + (x + 1)
= -(-1) + (-1 + 1) = 1 + 0 = 1
If x = -2, -x + (x + 1)
= -(-2) + (-2 + 1) = 2 + (-1) = 1
If x = -3, -x + (x + 1)
= -(-3) + (-3 + 1) = 3 + (-2) = 1
If x = -4, -x + (x + 1)
= -(-4) + (-4 + 1) = 4 + (-3) = 1
If x = -5, -x + (x + 1)
= -(-5) + (-5 + 1) = 5 + (-4) = 1
It is an identity.
ii. -x + (x + 1) + (x + 2) – (x + 3) = 0
If x = 1, -x + (x + 1) + (x + 2) – (x + 3)
= -1 + (1 + 1) + (1 + 2) – (1 + 3)
= -1 + 2 + 3 – 4 = 0
If x = 2, -x + (x + 1) + (x + 2) – (x + 3)
= -2 + (2 + 1) + (2 + 2) – (2 + 3)
= -2 + 3 + 4 – 5 = 0
If x = 3, -x + (x + 1) + (x + 2) – (x + 3)
= -3 + (3 + 1) + (3 + 2) – (3 + 3)
= -3 + 4 + 5 – 6 = 0
If x = 4 -x + (x + 1) + (x + 2) – (x + 3)
= -4 + (4 + 1) + (4 + 2) – (4 + 3)
= -4 + 5 + 6 – 7 = 0
If x = 5, -x + (x + 1) + (x + 2) – (x + 3)
= -5 + (5 + 1) + (5 + 2) – (5 + 3)
= -5 + 6 + 7 - 8 = 0
If x = -1, -x + (x + 1) + (x + 2) – (x + 3)
= -(-1) + (-1 + 1) + (-1 + 2) – (-1 + 3)
= 1 + 0 + 1 – 2 = 0
If x = -2, -x + (x + 1) + (x + 2) – (x + 3)
= 2 + (-2 + 1) + (-2 + 2) – (-2 + 3)
= 2 + -1 + 0 – 1 = 0
If x = -3, -x + (x + 1) + (x + 2) – (x + 3)
= 3 + (-3 + 1) + (-3 + 2) – (-3 + 3)
= 3 + -2 + -1 – 0 = 0
If x = -4, -x + (x + 1) + (x + 2) – (x + 3)
= 4 + (-4 + 1) + (-4 + 2) – (-4 + 3)
= 4 + -3 + -2 – (-1) = 0
If x = -5, -x + (x + 1) + (x + 2) – (x + 3)
= 5 + (-5 + 1) + (-5 + 2) – (-5 + 3)
= 5 + -4 + -3 – (-2) = 0
It is an identity.
iii. -x – (x + 1) + (x + 2) + (x + 3) = 4
If x = 1, -x – (x +1) + (x + 2) + (x + 3)
= -1 – (1 + 1) + (1 + 2) + (1 + 3)
= -1 – 2 + 3 + 4 = 4
If x = 2, -x – (x + 1) + (x + 2) + (x + 3)
= -2 – (2 + 1) +(2 + 2) + (2 + 3)
= -2 – 3 + 4 + 5 = 4
If x = 3, -x – (x + 1) + (x + 2) + (x + 3)
= -3 – (3 + 1) + (3 + 2) + (2 + 3)
= -3 – 4 + 5 + 6 = 4
If x = 4 -x – (x + 1) + (x + 2) + (x + 3)
= -4 – (4 + 1) + (4 + 2) + (4 + 3)
= -4 – 5 + 6 + 7 = 4
If x = 5, -x – (x + 1) + (x + 2) + (x + 3)
= -5 – (5 + 1) + (5 + 2) + (5 + 3)
= -5 – 6 + 7 + 8 = 4
If x = -1, -x – (x + 1) + (x + 2) + (x + 3)
= -(-1) – (-1 + 1) + (-1 + 2) + (-1 + 3)
= 1 – 0 + 1 + 2 = 4
If x = -2, -x – (x + 1) + (x + 2) + (x + 3)
= 2 – (-2 + 1) + (-2 + 2) + (-2 + 3)
= 2 – (-1) + 0 + 1 = 4
If x = -3, -x – (x + 1) + (x + 2) + (x + 3)
= 3 – (-3 + 1) + (-3 + 2) + (-3 + 3)
= 3 – (-2) + – 1 + 0 = 4
If x = -4, -x – (x + 1) + (x + 2) + (x + 3)
= 4 – (-4 + 1) + (-4 + 2) + (-4 + 3)
= 4 – (-3) + – 2 + (-1) = 4
If x = -5, -x – (x + 1) + (x + 2) + (x + 3)
= 5 – (-5 + 1) + (-5 + 2) + (-5 + 3)
= 5 – (-4) + -3 + (-2) = 4
It is an identity.