
Multiplication PrincipleMultiplying (or dividing) the same nonzero number to both sides of an equation does not change its solution set. Example: _{} so if 6x = 12, then 18x = 36 for the same value of x (which in this case is x = 2). The way we use the multiplication principle to solve equations is that it allows us to isolate the variable by getting rid of a factor that is multiplying the variable. Example: 2x = 6 To get rid of the 2 that is multiplying the x, we can divide both sides of the equation by 2, or multiply by its reciprocal (onehalf). Either divide both sides by 2:
_{} or multiply both sides by a half: _{}
Example: _{} Multiply both sides by the reciprocal of the coefficient, or _{} _{} 
