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.
