Algebraic Proofs Examples
Example 1
Write a proof for the statement "If 2x – 7 = 13, then x = 10." Which properties are used the proof? 
Example 2
Find the error in the following "proof" of the statement, "If 3 + z^{2} = 28, then z = 5." Then, find a counterexample to the statement itself.

Example 3
Write a proof for the statement "If x^{3} + y = 10 and 3(3x – 3) = 9, then x = y." 