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Lesson 105: Intro to Algebra (Part 1)
We use algebra to find the value of variables in equations. Once you learn some procedures, it's easy to do. It's also easy to check your answers.
Take a look at this equation: x - 5 = 2. It's called an equation because it has an equals sign. x is called a variable. That means it can represent different numbers in different equations. We didn't have to use x. We could have used any letter, or even a special symbol, but quite often, x is used. Our task is the find the value of x in this equation.
In this equation, it's very easy to figure out the answer. x is 7. You can do it in your head. But, if the numbers were more complicated, we would need a procedure to use. Here is what we do. We want to try to isolate x by itself on one side of the equal sign. Once it's by itself, it's value will be obvious.
We're allowed to do whatever we want to one side of the equation, as long we do the same thing to the other side. What can we do to get x by itself? We need to see what is happening with the x. We're subtracting 5 from it. What is the opposite of subtracting 5 from a number? It's adding 5. Addition and subtraction are inverses of each other.
It's helpful to set up the equation like this:
x - 5 = 2
+ 5 +5
---------
x = 7
You can see that the -5 and +5 add to 0, and therefore are eliminated. Students sometimes refer to this as canceling out. We're left with x = 7. It's very important to always check your answer. Sometimes a test question will tell you to show your check, and you'll lose points if you don't. All you do is substitute ("plug in") your answer into the original equation, and see if it works. 7 - 5 = 2? 2 = 2. It checks.
In the next lesson, you'll learn how to work with problems that involve addition, multiplication, and division. You'll have more practice with this later. Be sure to memorize the procedure shown.
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