Linear Equations are
equations involving multiplying
and adding and subtracting
that have no exponents.
You can always solve them
by repeated use of a very
simple idea.
If two things are
equal and you do the same
thing to both of them,
then they must still be
equal.
The game in solving equations
is to keep doing this
until you get the variable
alone on one side of the
equation and a number
on the other side of the
equation, and then for
the original equation
to be true, this equation
has to be true, and this
equation tells you exactly
what the variable has
to be. The only other
trick is to decide what
operations to do to both
sides to get it into this
form. To do this, you
need to think ahead a
little bit and also keep
your goal in mind. Always
remember that in the end
you are trying to get
the variable alone on
one side of the equation
and a number on the other
side. If there is an operation
done and you want to get
rid of it, the best way
normally to do this is
to do to opposite operation.
If you have several operations
being done to the variable
it normally works best
to get rid of the last
one done first. Put yourself
in the place of the variable
and ask if I was the x
what is being done to
me first and when you
are doing this remember
the order of operations.
A general procedure that
will always work with
these problems is to first
simplify both sides of
the equation, and then
get all of the variables
on one side and all the
numbers on the other side,
and then divide by the
coefficient. But other
methods will work as well.
