To obtain the solution set of an equation it is often necessary to transform it into a simpler form in which the solution is easily seen. The expressions on either side of the equality symbol can be reduced to their simplest form. Additionally, the following operations transform an equation into an equivalent equation:
a = b is equivalent to: a + c = b + c
a = b is equivalent to: a - c = b - c
a = b is equivalent to: a × c = b × c, c ≠ 0
a = b is equivalent to: a ÷ c = b ÷ c, c ≠ 0Note that neither raising both sides to a power nor finding the same root of both sides will always yield an equivalent equation. The former operation may introduce extraneous solutions while the latter may obscure valid solutions. For example, the equation:
4x2 = 100This has the solution set {-5, 5}. Taking the square root of both sides gives the equation:
2x = 10This has the solution set {5}.