A linear
equation involves variables whose
exponents are "1."
A linear equation will also
contain constants named with letters
and/or numbers.
Solving a linear equation
refers to writing an expression with the
variable or constant in question on the
left hand side of the equals sign with
everything else on the right hand side of
the equals sign.
For example:
given the equation 3y -
2 = k - 36
"solve for y"
1) add 2 to
both sides of the equation:
3y = k - 34
2) divide both
sides of the equation by 3:
y = (k - 34) / 3
Now, how is it that I knew these 2 steps
to solve for y?
Lots of
experience? (well maybe)
Lots of
intuition? ( perhaps
some, comes with experience right?)
Let's stop right here! This is an
issue I have with modern day math texts
used in our classrooms. The more I
see these texts, most written by the
professionals, you know, the
educators in the classroom to the lofty
doctorate towers of our universities, the
more I desire to throw them headlong
toward these authors, hopefully to knock a
bit of sense into them!!!
These texts assume that the student,
has a gifted mathematical aptitude for
doing problems like these equations in
their heads.... "just figure it out" is
their motto. Well guess what?
Very very few children are a Gauss, or an
Euler, or a Hawkins!!!! Have you
seen the "sidebars" placed between the
paragraphs in these texts? Doing a
geometry proof requires concentration not
constant distraction!
I watched my daughter struggle with
solving an equation in her 6th grade text,
her introduction to a simple equation was
to use intuition to solve for one of the
'letters." I helped her get
past
it and dried her tears. I took
a further look at that "math text" and go
so irritated I threw it across the
room.
If you are a home-schooler I strongly
advise using of the Saxon Math Program.
It is by far the best I've seen yet.
Ok,
computer programs have been written to
solve linear equations. There is no
mystery involved, no inexplicable
intuition which only a few have. On the
contrary, here is a step by step method
that will solve any linear equation.
1) Reduce all fractions
2) Eliminate all grouping symbols
3) Isolate the unknown to one side
of the equation
4) Factor out the unknown
5) Divide by the coefficient of the
unknown
6) Reduce all remaining fractions
7) Simplify the result
Now for the
examples.
Math is a
step-by-step process. Every step
must be preceded by a valid step.
The student should show every step to
solve an equation, period.
Also, lining up the equal signs from step
to step helps organize the work.
Solve for x
in the equation z - 5hx
+ 6 = 3x + 10/2
1) reduce
all fractions
z - 5hx + 6 = 3x + 5
2)
unnecessary
3) isolate
the unknown
subtract 3x from both sides
-3x +z -5hx + 6 = -3x + 3x + 5
-3x -5hx +z + 6 = 5
subtract z an 6 from both sides
-3x - 5hx + z + 6 -z -6 = 5 -z - 6
-3x - 5hx = -1 - z
4) factor
out the unknown
x( -3 - 5h) = -1 - z
5) divide of
coefficient
6) reduce
fractions
factor out a -1 from both the numerator
and denominator and cancel
7)
unnecessary
Note that in
the answer the z and h are listed first,
then the numbers 1 and 3. This is a
convention, that's all. (1+z)/(3 +
5h) is a valid answer as well.
This is another FREE ALGEBRA PRINTABLE presented to you from the
Algebra section of
K12math.com