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Now that you know about Equations and Negative numbers, you need to know how to solve equations.
Lets start with the most basic addition problem again. 1 + 1 = xNow, I know the answer is very very obvious. But I am trying to teach you how to use equations. My Algebra teacher would give me bad grades, because I could see the answer without using the Algebraic solving method. You need to show all your work for now, because It gets complicated later. The first thing to do with the equation is to simplify it. Right now it is more complicated than it needs to be. Notice the 1 + 1. Those numbers can be added. It will not make the equation "Un-balanced". So, lets add 1 + 1. Our new equation looks like this:
2 = xActually, we have already solved the problem. x = 2! Usually we put the variable first, then the value of the variable, but we know that it is the exact same thing.Simplifying is not limited to addition. Any numbers that you are supposed to divide, multiply, subtract, square root or whatever, can be simplified without worry. Consider the following: 50(1 / 2) = 50[(x - 1) /2]We can simplify it to a simple equation. But where to start? Remember that when a number is next to a parentheses it means multiply it by what's in the parentheses? So, just looking at the left of the equation right now, can we first multiply 50 by 1? No. 50 must be multiplied by everything inside the parentheses. We must first find out what 1 / 2 is. Then multiply 50 by that. How can you figure out what order to do things in when it gets complicates? There is a specific order. Always do things in parentheses first. You can at first treat them as separate equations. Then the stuff in brackets. Then, once you are in the parentheses, do all the exponents first. Then multiplication, then division, then addition, then subtraction last. Always in that order(treat brackets as parentheses). The way to remember this order is Pemdas. The first letters of:
50(1 / 2) = 50[(x - 1) /2]Let's work on the left side first, just because. PEMDAS tells us to first go in the parentheses. (1 / 2)We do the only operation there is, and divide one by two. This gives us .5 or one half.
( .5 )Now we can look at the rest of the left side again, with a new value for the parentheses: 50( .5 )So we multiply 50 by .5 . Later you will be able to know that this is the same as dividing 50 by 2(50 one half times, or 50 of one half)You will be able to do it in your head after a bit of experience. But as for now, use the calculator. The answer is 25. So we have one side of the equation simplified.
25 = 50[(x - 1) / 2]Now for the right side. Remember PEMDAS? Parentheses first. In this case, there are brackets, which are just like parentheses. We look at just what's in them [ (x - 1) / 2 ]Now we just look at the parentheses. (x - 1)What is x - 1? Well, we don't know! We don't know the value of x! We cannot simplify! We must go back.
25 = 50[(x - 1) / 2]This equation is still complex, and we can not use basic operators to make it any more simple. We must add our own operations to simplify. But if we did that, the equation would no longer be equal, so we must use the operation on both sides of the equation. We start outside the parentheses, and divide both sides by 50. 25 = 50[(x - 1) / 2] Now our equation looks a little nicer. Lets wrestle with it some more. Just use the opposite operation as the number you want to get rid of. For example, I want to get rid of /2 right now. .5 = (x - 1) / 2 Now add two to each side. 1 = x - 1If you want x on the other side, subtract x from both sides, then 2, then multiply the equation by negative one. It will look like x = 2. So we have simplified our equation, and found the answer. In case you did not notice, the equation was exactly the same as:
1 + 1 = xJust manipulated around. Go ahead, on a piece of paper, try to manipulate the equation to look like that. It should be fairly simple. You can also just skip the initial steps I showed you and start manipulating the equation from this point: 50(1 / 2) = 50[(x - 1) /2] |