Algebra

The Unknown

Usually, in Algebraic equations - in fact, all the time - there's an unknown value, and you have to figure out its identity. It is usually represented by a letter like x.

Here's an example of where you may see an unknown:

Question 3: A square has a side length of 3 units. It's area x units squared. Solve for x.

We know that the area of a square is just its side length squared. The side length, in this case, is 3 units. So we can make the following valid equation:

x units squared = (3 units) ^ 2

We can do this because x is the area of the square and the side length squared is also the area of the square. So essentially we are saying:

The area of the square = The area of the square

And this is a valid equation. So back to the original equation:

x units squared = (3 units) ^ 2

We can evaluate the right-side expression to get:

x units squared = 9 units squared

So now we know that x has to be 9.

x = 9

Here is another example question:

Question 4: I have 3 green apples and 2 red apples. I have y green and red apples. I need to solve for y.

In this question, the unknown is y. We need to solve for y, which is denoted as "the number of apples that are green and red". And logically, this is the same as "the number of green apples plus the number of red apples". So we get this:

y = The number of green apples + The number of red apples

Luckily, we are given the number of green apples and we are given the number of red apples. So we get:

y = 3 + 2

y = 5

So the answer is 5.

I know that Algebra was unnecessary in these questions, but the purpose of these questions was to make you understand what an unknown is.