Which equation is an identity?
a. 7m – 2 = 8m + 4 – m
b. 8y + 9 = 8y – 3
c. 11 – (2v + 3) = –2v – 8
d. 5w + 8 – w = 6w – 2(w – 4)

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.

If you need an equation, it would be y=2x+8, y would be how long it grew, x being weeks.if you need how long he was asleep, it would be 4 weeks if he started with no beard, the equation would be x=8÷2if he did have a beard before hand, the equation would be 2w+x=8