# lorem ipsum

Doing the same thing to both sides of an equation does not necessarily result in something useful or equivalent. For example, if we are given that 3x + 1 = 16, and we want to know what x is, multiplying both sides by 0 results in the equation 0 = 0, which is neither useful, nor equivalent to the original equation. For another example, if we are given that sqrt(x) = x – 2, and we want to know what x is, squaring both sides gives x = (x – 2)^2, which is useful, but is not equivalent to the original equation.
Sometimes the procedural rule is promulgated that you are to change only one side of an equation (until it matches the other side), because that insures that every step is equivalent to the original equation, but that does not apply to what we are considering here, because what we are considering here are called ‘conditional’ equations, whereas the procedural rule of changing only one side of an equation is for proving identities (typically, trigonometric identities).
keywords: Mathematics, solving equations