|
Suppose
you were given an equation
like
2x – 3 = 5.
You
will need to use the addition
principle to move the –3,
and the multiplication principle
to remove the coefficient
2. Which one should you use
first? Strictly speaking,
it does not matter—you will
eventually get the right answer.
In practice, however, it is
usually simpler to use the
addition principle first,
and then the multiplication
principle. The reason for
this is that if we divide
by 2 first we will turn everything
into fractions:
Given:
2x – 3 = 5
Suppose
we first divide both sides
by 2:
Now
there is nothing wrong with
doing arithmetic with fractions,
but it is not as simple as
working with whole numbers.
In this example we would have
to add 3/2 to both sides of
the equation to isolate the
x. It is usually
more convenient, though, to
use the addition principle
first:
Given:
2x – 3 = 5
Add
3 to both sides:
At
this point all we need to
do is divide both sides by
2 to get x = 4. |
