
Actually, as much as it might surprise
you, we've been doing algebra right here.

These 2 symbols, the square and the
triangle that we assigned to replace the

words that we had written earlier are
called variables. In algebra we make a

distinction between numbers and variables.
Numbers are well, numbers, like 3,000,000

or 100,000, and variables are generally
represented by symbols or single letters.

A variable doesn't have a set value like a
number does. Instead, it's value is

allowed to vary depending on what we
decide that it should equal. We'll talk more

about how we make decisions about that
soon. Numbers will appear either as

constant terms on their own, just numbers
like 3,000,000 right here, or in terms

that combine numbers and variables like
this last one on the right. When

multiplied by a variable or set of
variables, a number is called a

coefficient. So again, going back to our
variables, I could of chosen any two

symbols I wanted to represent these two
quantities right here, the square and the

triangle. I didn't have to choose the
triangle and I didn't have to choose the

square. In fact picking these two
particular symbols, is actually pretty

unconventional in math. To give you a
preview of what you're usually going to be

seeing during this course, I'll write this
equation out with more typical notation.

We'll most often see the letters X and Y
as your variables in equations in algebra.

You can also see I've removed the dollar
signs and the commas from the original

equation down here to make this equation
look a little bit more clean and strictly

mathematical. You'll notice that I also
sneakily deleted the multiplication sign

we had in the top equation, and didn't
write it down here at the bottom. When we

have single terms that involve both
numbers and variables multiplied together,

we don't usually write the multiplication
sign in, like I did at the top. As long as

we write the symbols directly next to each
other, with nothing in between,

multiplication is assumed to be happening
between them. It's like there's an

invisible multiplication sign written
right here. I'm going to erase that

though, to remind us that we're not
usually going to see any multiplication

signs written between numbers and
variables. Although people doing math

often use the variables y and x in their
equations, I really want you to remember

that this is not necessary. Triangles and
squares are just as useful as x's and y's.

No matter what symbol you choose to write
a variable with, the power that it has is

still the same. It acts as a slot where we
can insert different numbers to make terms

and expressions take on different values.
So maybe I set this first variable equal

to 3 and the second equal to 1 or
maybe this is 1/2 and this is 23.

In certain situations, there will be
restrictions placed on what different

variables can equal. But, until we have
more information about what they equal, we

leave them written as variables, showing
that their values are still sort of a

mystery to us.