A Primer in Finding X

Algebra is all about different ways to rearrange equations so you can isolate different variables or terms. Often we call this finding x.

Most students find this challenging the first time they see it. Until this point everything has been done using concrete numbers. But now, we are using variables to find numbers. It can be confusing. 

I can’t cover everything you need to know about how to find x, but I can give you a primer so you have a decent place to start. I will go into further depth in other posts.

x is a number

The first thing every student should understand is that we use letters, like x and y, to stand in for variables we don’t know yet. That means x, y, or any other letters in an equation are numbers. 

What do those numbers mean? That depends on the context.

If you have a word problem, then the x and y are standing in for a particular kind of number. For example:

The cost to rent a car starts with a flat fee of $25 plus 30 cents per mile driven. How much does the car rental cost if I drive 100 miles?

For this kind of word problem, we know that $25 is a flat fee, so it gets added on at the end. 30 cents per mile means we multiply 30 cents times x number of miles. Y would then be the total cost of the rental. So your equation would look like this:

total cost = 0.30 (number of miles driven) + 25

       y       = 0.30                   x                    + 25

When we write out our equation like this, it is easy to see what x and y are representing. Y is standing in for the total cost of renting the car, and x is the number of miles driven.

But what if you just have an equation? What if there is no context? You can make your own context if it helps you to keep the variables straight.

Simple steps for solving for a variable

Solving for a variable or term is actually fairly simple and can be boiled down to a number of steps. They are:

1. Identify and highlight what you need to solve for
2. Use PEMDAS in reverse order to increasingly isolate what you want
3. Do any arithmetic or simplifying to get a final answer 
4. Done

Notice how you don’t do arithmetic while you are isolating the variable? Waiting until the end helps to reduce silly 2*3=5 type mistakes. It also shows your teacher if you took the right steps, which will help you get a higher grade if you make a silly math mistake.

While this is simple to say, it is harder to execute. Here are many example problems to help you get the feel for how to do this. 

I recommend working on the problems with me. After the first few examples, pause the video and try to solve the problem on your own. Then play it again to see how you did.

This is going to be a bunch of mixed practice. I will go into patterns for individual problem types later.

Examples

For more examples, check out the STEM911 YouTube Channel.