Intro to Equations

First: you should know the computer characters for all the mathematical symbols.

Add
Subtract
Multiply
Divide
Exponent
Equals
Variables +
-
*
/
number2
=
x, y, z etc....

Let's start with equations. You know what an equation is. Everyone has seen them. Einstein's famous Relativity equation for example:

E=mc2
Whether you know it or not, you have worked with equations. Consider the first question your math teacher gave you:

1 + 1 = ___
The answer is 2, and we can re-arrange that too, right?

1 + ___ = 2
Same equation, right? We can also do this:
2 = 1 + ___
they all are the same equation, we just have to find different parts of it. In algebra we call the number we are trying to find a variable. All the places you see the underline, that is the variable. Except we don't use underlines in Algebra, we use little letters to take the place of the underline. Usually, we use the letter x. This is just a letter that means "We don't know exactly what goes here, but we are working on it.". We can re-write out basic equation like this:
1 + 1 = x
It means the exact same thing as above. We know that x is 2. The answer is also an equation!
x = 2
Sometimes, with big complex equations, we can not figure out the equation that fast. In case of this, there are some special tricks Mathematicians have come up with over the years. Now all students are taught this exact method of working with equations. This is called Algebra.

Taking out basic addition problem, there are actually several ways to look at it. First, we can see it like this:

1 + 1 = x
We can also see it like this:

x = 1 + 1
Same thing, right? Now look at this:

1 = x - 1
This is where it gets tricky, We already know that x is 2. So look at the equation, mentally take out x and replace it with 2. Do the math;

1 = 2 - 1
Two minus one is one, right? This leaves us with:

1 = 1
This is obviously true. But how did I make that equation?
I moved the one from the left side, and put it on the right side. How did I do that?
It is really simple actually. because what is on one side of the equals sign is always equal to what is on the other side, we can change the equation, as long as we keep both sides equal. So I can subtract one from each side. If I were to take one from the left side, but not the right, it would not be equal. So I need to take one from both sides of the equation. It will always work out to be equal if you do this.
I am not limited to subtraction only though. I can change the equation any way I want, as long as I do it the same way to both sides. If I want to make my basic addition equation look really complicated, I can do all kind of neat stuff to it.




1 + 1 
 = 
x 
   ::   Original Equation


  -1 
   
  -1 
   ::     Take 1 from both sides


1
 = 
x -1
   ::   New Equation


 / 2 
   
  / 2 
   ::     Divide both sides by 2


1 / 2 
 = 
(x -1) / 2
   ::   New Equation #2


 * 50 
   
  * 50 
   ::    Multiply both sides by 50


50(1 / 2)
 = 
50[(x - 1) /2]
   ::   New Equation #3

You see how complicated a simple equation can become. But if you were to work through it, you would eventually come up with the equation
2 = x or

x = 
2

You may be confused by the syntax I used. It is standard syntax, and important to know. You can group numbers together so that you know to treat them together. It is very important we make it clear it is a group. More on this in the Problem Solving lesson. When a group is in parentheses ( "( )" ), or brackets ( "[ ]" ), you know that any number next to it is automatically multiplied, unless it says to do otherwise. This is just a shortcut. Some people will actually put the dot* that means to multiply in, when they write it out, but it is not necessary.
Brackets are used if there are already parentheses inside.

*The Multiply dot is a small dot right in the middle of the text line, like a subtract, except only a dot. It means the exact same thing as the "Multiply" XThere is no key or it on the keyboard, so we use the "*" sign.