An identity is obtained when you substitute any value of x to an equation, both sides will give out the same answer. A trial-and-error method is best used for questions like these. The method is shown below:
Let: 1 = m = y = v = w
A. 7m – 2 = 8m + 4 – m
7(1) – 2 = 8(1) + 4 – (1)
5 =/= 11
B. 8y + 9 = 8y – 3
8(1) + 9 = 8(1) - 3
17 =/= 5
C. 11 – (2v + 3) = –2v – 8
11 - (2(1) + 3) = -2(1) - 8
6 =/= -10
D. 5w + 8 – w = 6w – 2(w – 4)
5(1) + 8 -1 = 6(1) - 2(1 - 4)
12 = 12
Therefore, the choice D is the identity.
