Question

Identify the identities from the following by replacing the variables with the values 0, 1, 2 and 3.

(6) n + 5 = 2 (n + 2) − n + 1

Answer 1

n + 5 = 2 (n + 2) − n + 1
Substitute n = 0
LHS : n + 5
= 0 + 5
= 5
RHS : 2 (n + 2) − n + 1
= 2 (0 + 2) − 0 + 1
= 2 (2) + 1
= 4 + 1
= 5
∴ LHS = RHS for n = 0
Substitute n = 1
LHS : n + 5
= 1 + 5
= 6
RHS = 2 (n + 2) − n + 1
= 2 (1 + 2) − 1 + 1
= 2 (3) − 1 + 1
= 6 − 1 + 1
= 5 + 1
= 6
∴ LHS = RHS for n = 1
Substitute n = 2
LHS : n + 5
= 2 + 5
= 7
RHS: 2 (n + 2) − n + 1
= 2 (2 + 2) − 2 + 1
= 2 (4) − 2 + 1
= 8 − 2 + 1
= 6 + 1
= 7
∴ LHS = RHS for n = 2
Substitute n = 3
LHS : n + 5
= 3 + 5
= 8
RHS : 2 (n + 2) − n + 1
= 2 (3 + 2) − 3 + 1
= 2 (5) − 3 + 1
= 10 − 3 + 1
= 7 + 1
= 8
∴ LHS = RHS for n = 3
As LHS = RHS for all the values of n,
n + 5 = 2 (n + 2) − n + 1 is an identity.