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 different form. What you get if you a given

2 apples + 3 peaches + 4 apples + 2 lemons + 2 peaches + 3 lemons

Now anyone can give correct answer:

2 apples + 3 peaches + 4 apples + 2 lemons + 2 peaches + 3 lemons =
6 apples + 5 peaches + 5 lemons

How one gets the answer? Find total number of apples, find total number of peaches and find total number 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 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.

Scale

There is an equation 2x - 15 = 3x - 10 Let's try solve it. Let us add 15 to both sides of the equation.

2x - 15 + 15 = 3x - 10 + 15

-15 and + 15 gives 0. -10 and +15 gives 5

Now we can rewrite the equation in more simple 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 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 what x equals 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.

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