Thinking in Algebra

Read this only if you are a beginner; otherwise, you should be able to easily think in algebraic terms

Looking at these images, algebra may seem dauntingly difficult, but algebra is just applied arithmetic. You may have done problems where you had to deal with finding unknown values, but if you have not, here is a way to think about that kind of problem.

You know that one plus one is two, and two plus two is four, but three plus what equals six? In number form this is written as

3+what=6

This is simple you may say, I just subtract three from six! It's just common sense, and you arrive at the conclusions that 3+3=6. What if I told you, that is Algebra you just done! You may be familiar with guess-and-check, inverse operations, tape diagrams, or working backwards to solve problems like this. As you go on, however, there is another major tool you can use to solve problems like this, and that is Algrebra.

Let's write this equation out again, but we make "what" a single-letter variable.

x+3=6

Now, if we isolate x and have another number on the right side, we can have an equation directly saying what x, the term we want to find, is. How do we do that is the problem. Simply look at the left side, the side with the x. Without the three, then it can be pure. 

How do we do this? Well, you have probably heard of opposites. The opposite of an arbitrary number x is -x. You may realize that these two numbers add up to exactly 0. It is just the basic rule that anything that is subtracted from itself results in the number 0.  How does this connect with our problem? Well you see, we are trying to isolate x, trying to make it 0 except for x. Therefore, we can simply subtract 3 or add 3, opposite, -3, to the side x+3. However, we need to keep both side equal, so we need to make this change from both sides, so now we have this:

x=6-3

Which simplifies to 

x=3.

We have now used algebra to solve this math problem of basic algebra. This may seem difficult and unnecessary, but in many equations, algebra is the only simple option, and repetition can help you get used to this technique. For more of what you just did, go to "Linear equations"