# Limit proofs

I just have a general question about limit proof using epsilon delta proofs

It generally follows the algorithm from this website:http://www.milefoot.com/math/calculus/limits/DeltaEpsilonProofs03.htm

focusing on the first example(example using linear functions)
The first table I get, but is the second table necessary, it basically restates the given?
it seems analogous to x + 1 = 3
x = 2
and then subbing 2 in for x