Hey it’s Professor Dave, let’s learn some algebra.
When you learn math in school, up until a certain point, it’s just called math.
Then all of a sudden, one day, math class isn’t just math, it’s called algebra.
Although it may seem scary to graduate from plain old math to algebra, it won’t be so
daunting once we realize that algebra uses symbols just like arithmetic does, and it
is quite easy to make these symbols intuitive so that you can manipulate algebraic equations.
Let’s start out by discussing that algebraic essential, the unknown variable.
First of all, what is a variable?
In math, a variable is a letter or symbol that represents a quantity that can change.
This is different from a constant, which is a letter or symbol that represents a quantity
that does not change.
A variable can be just about anything.
The inches of rain in your town in a particular month, the price of gasoline, the speed of
a plane, whatever it is that you want to do math with.
Whereas with arithmetic our equations simply contain numbers and arithmetic operations,
an algebraic expression will always include one or more variables, as well as some numbers
and operations.
For example, 3x + 2 is an algebraic expression.
We can evaluate this expression for any value of x that we choose, we simply plug the value
into the expression, understanding that we can now represent the multiplication of two
numbers by simply placing them next to each other.
We could make a table as we do this.
When x is one, we replace the x with a one.
Three times one is three, plus two is five, so when x is one, this expression is equal
to five.
When x is two, we get six plus two, or eight.
When x is three, we get nine plus two, or eleven, and so forth.
This is useful, because we can use algebraic equations to model real-world situations and
make meaningful statements about them.
Instead of just using arithmetic to say that five cheeseburgers, at three dollars each,
will cost a total of fifteen dollars, we can set up an algebraic relationship that allows
us to do a wide variety of calculations that are pertinent to this situation, like how
Y, the total cost, is equal to three times X, the number of cheeseburgers.
The trick is just knowing how to set up the equation.
Let’s say that you love to watch TV, but not as much as your friend, Bobo.
However many hours of TV you watch in a day, Bobo watches twice as much plus an additional
hour.
Well if you watch X hours of TV, and Bobo watches Y hours of TV, we can relate X and
Y with an equation just like we did for the burgers, where Y equals 2X plus one.
Whatever you watch, which is represented by X, we double it and add one to get Y, the
amount Bobo watches.
While that was a pretty trivial example, these kinds of algebraic relationships allow us
to do some pretty powerful things.
Before we start doing lots of algebra, there’s a bit more to learn about algebraic properties,
so let’s move forward now.