How to Understand Algebra
Ask a person who has never studied algebra to solve the following problem:
2X + 3Y + 4X + 2Z + 2Y + 3Z=?
This person will be confused and not be able give the correct answer, though s/he knows it, only s/he does not realize that s/he knows it because s/he is scared by the form of the question.
Want to see the proof?
Ask the same question in a different form. What you get if you are given
2 apples + 3 peaches + 4 apples + 2 lemons + 2 peaches + 3 lemons
Now anyone can give you a correct answer:
2 apples + 3 peaches + 4 apples + 2 lemons + 2 peaches + 3 lemons =
6 apples + 5 peaches + 5 lemons
How one gets the correct answer? Find total number of apples, find total number of peaches and find total number of lemons. Do you have to know algebra? No. You can use common sense.
Using common sense, solve the first problem: Find total number of X, Find total number of Y, Find total number of Z
2X + 3Y + 4X + 2Z + 2Y + 3Z=6X + 5Y + 5Z
What is algebraic equation? You may think of it as of a scale. The "=" sign tells us the scale is balanced. If you place a weight on the left plate of the scale it will go down and then the right plate will go up. To balance the scale you have to place the same weight on the opposite plate.
There is an equation 2x - 15 = 3x - 10 Let's try to solve it. Let us add 15 to both sides of the equation.
2x - 15 + 15 = 3x - 10 + 15
-15 and + 15 gives you 0. -10 and +15 gives you 5
Now we can rewrite the equation in more simple and convenient way:
2x + 0= 3x + 5 or 2x = 3x +5
Again let us remove the same weight from the opposite plates of the scale so that balance will not be destroyed. Subtract 3x from the left and the right side of the equation.
2x - 3x = 3x + 5 - 3x.
2x -3x gives -x. 3x - 3x gives 0.
Now we can rewrite the equation in more simple way:
-x = 5
To find x multiply both sides of equation on -1
(-x ) * (-1) = 5 * (-1 )
x = - 5
Now you not only solved the algebraic equation, but also prove to yourself that you can understand algebra.
In my tutorial, that I wrote for my daughter there are 80 algebraic equations with answers, solutions and explanations. I guarantee that after reading my explanations and doing my exercises you will understand and love algebra. It is only 24 pages. It will not take much of your time. Buy it as ebook in PDF format just for $7.00 Download
To pay via Twitpay you have to registered on Twitpay
It's simple to use. All you need is a Twitter account and a PayPal account.
You have to register on Twitter for many reasons. Visit that link to know why.
You can register to my new web site Algebra Exercises Online Center and practice in solving algebra equations
| Home | Copyright 2006 by Sergey Skudaev.All right reserved. Contact us |