Variables

Before Algebra, we've seen unknown values represented by a fill-in-the-blank or a box.

It means "something" + 2 = 7. We just need to find what that "something" is to make the equation true.

However, there are two main problems with this :

1. What is we had to write a lot of these somethings

2. What is we had to differentiate between the unknowns

So, is there an easy way to write and differentiate between a lot of unknowns? Yes, with variables!

A variable is basically just a symbol it can be a special character, but most often it is a letter.

Examples :

a, b, c, x, y, z

Let's illustrate how we would use a variable.

Imagine we have some number of cows. We don't know how many, but there are cows.

We know that by adding 3 we get 10.

How would we figure out the amount of cows?

The first step is recognizing that the cows are a variable because they are an unknown.

To solve the equation imagine we are trying to use a balance.

Whatever we do to one side, we have to do with the other.

To get the cow by itself we have to get rid of the +3; the simple way to do this is find the opposite of +3, which is -3.

If we subtract -3 from both sides (because we are trying to keep a balance) :

On the left side we can simplify +3 and -3 to 0, and on the right side we can simplify the 10 and -3 to 7.

Now we know that there are 7 cows!

Variables have a special property, you can combine them.

If you have multiple of the same type of variable you can add them up.

Example :

If we have two x's we can combine them because the variable is the same.

We do this by adding the coefficients (the numbers in front of the variables).

*Don't forget, x is the same as 1x

The coefficient represents how many of that variable there are.

2x is equal to x + x

So, by adding the coefficients 2 and 1, we get 3.

To find out what x is we have to get it alone.

Remember the rule to find the opposite, 3x is the same as 3 times x.

The opposite of multiplication is division so we have to divide by 3 to get x alone.

3 over 3 is simply 1, so it cancels out as it does not affect the x.

Finally, we can simplify the righthand side of the equation and get that x equals 1.

Now we now how to solve an equation with a variable, but what if we have two variables. There is an interesting thing you can do with variables.

If you know the value of one variable, you can plug that in and then solve for the other.

Example :

In later lessons we'll learn how to solve an equation without that given.