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Homework Help: Math: Algebra: Introduction to Algebra (page 3)
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 The next step in
algebra is learning about a variable. Variables are defined as
numbers that can change value or represent a missing value. The
empty box in our last equation was a variable, but drawing cute
little shapes can get tiresome. Variables are usually represented
by letters of the alphabet, and for whatever reason x, y, and
z are the most commonly used variables. Here's how our last equation
would look using a variable:
Notice
that the 'x' is a variable, NOT the multiplication sign. It is
customary in math to use the * sign to represent multiplication
so that variables don't get confused with operations. Our goal
in the equation is to solve for the variable x, and you might
be able to do so using trial and error, but there is an easier
way. Since we have a balanced equation, we can do anything to
one side, but we have to do the same to the other side. For instance,
we can add 1 to each side, resulting in 4+x+1=3+3+1. Adding 1
to only one side would create an inequality, which is not what
we want.
The
best way to solve is by isolating the variable on one side of
the equation, so that we can tell what value it holds by looking
at the other side of the equation, as in x=4. To do this, we must
get rid of the 4. Since we can do anything to both sides
of the equation, why not subtract 4 from each side?
On
the left side of the equation, 4-4 is obviously 0, so we can get
rid of that, and 3+3=6, minus 4 is 2, so we can write 2 in place
of 3+3-4.
Remember-
the goal is to get the variable alone by doing the same thing
to each side. In an equation like 4x + 4 = 12, you would subtract
4 from each side to get 4x = 8. Divide each side by four and you've
got x=2. Now you've got a basic understanding of algebra, and
can solve equations like 7+x=14. If not, you might want to re-read
the lesson.
Copyright © 2002 Ted Wilcox
This lesson was reproduced on Jiskha Homework Help with permission from the author.
Homework Help: Math: Algebra
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