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Multiplying (or dividing) the same non-zero
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 (one-half).
Either
divide both sides by 2:
or multiply both sides by a half:
- Whether
you prefer to think of it as dividing by the number or multiplying by its
reciprocal is not important, although when the coefficient is a fraction
it is easier to multiply by the reciprocal:
-
Example:
Multiply both sides by the
reciprocal of the coefficient, or 
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