How to do algebra - Examples of algebra solutions

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 to give the correct answer, though she knows it, only she does not realize that she knows it because she 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? How to do algebra? 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.

Scale

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 proved to yourself that you know how to do algebra!

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