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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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