Why do we need algebra, what is it used for, who developed it and how do i use it?
In algebra we try to look for what we do not know based on information we have. We have equations which are statements of truths and our job is to find the unknown which will give us the "thing" we are looking for. In math, this unknown "thing" is a number. For example 5=5 is an equation and is a statement of truth. We also know that 3+2 = 5 another statement of truth.
Now lets image that we did not know that three plus two was five. The variable would be the unknown number we are tying to find. This would be that 3 + "something" = 5. Lets call that "something" the letter a so we do not have to write as much. This means that 3 + a = 5. The question now is, how do we find out what a is? To find a we have to isolate it so we can know what a equals. Right now we only know that a+3 is 5 but we do not know that a equals by itself. This is called isolation. We want to put our variable on one side of the equation.
Do you agree that if 10 = 10 then 10-1=10-1 so 9=9? Notice that if we subtract 1 from the right hand side we have to do it to the left hand side of the equation as well otherwise we do not have an equality. If we do not have an equality we will not have a true statement and so we will get the wrong answer. In light of this, what can do to our 3+a=5 equation so that a is by itself? Well w can subtract 3, 3+a - 3 = 5 - 3.
3+a-3 = 5-3
3-3 + a = 5-3
0 + a = 2
a = 2
As you can see we solved for a and it was suppose to be 2 as we saw earlier. What did we subtract 3 from both sides? Sure we wanted to isolate for a but was there another way to do it? Well not because notice that we are adding a and 3. The opposite of addition is subtraction that is why we subtracted. With that in mind lets try this next example,
4*a = 8
We have to isolate for a and we are multiplying by four. The opposite of multiplication is division so we need to divide by four. If we do that, here is what we get,
4*a/4 = 8/4
4/4 *a = 2
1*a = 2
a = 2