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Has to deal in the learning of proofing equations and understanding how to solve equations

### In the world of Real Number there are 14 properties

each one relates to its own rules and is used when proofing an equation

### Proofing

basically when you proof an equation, you are proving that you have obtained the right answer by completing the right steps in the right order in the right way

### Example;

if the property states that anything is equal to itself then that means 5=5, 5·1=5·1, 7-22=7-22, and 8+12=8+12

### Symmetric Property

if you switch the place of the variable from the left to the right&from the right to the left, the value stays the same; if X=B then B=X

### Example;

if the property states that if X=B then B=X and the value stays the same, that means if 5=X then X=5, and the value stays the same

### Transitive Property

a statement that includes if, and, and then; it takes two true statements and creates another sentence that is assumed to be true because it was formed with the information collected from the first two statements

### Example;

if a=5+c and b=5+c then a=b; we see that the variables [a] and [b] both equal [5+c] so we can assume that [a=b]; if a=5x+b and x=2+3 then a=25+b

### Substitution

simply for any two numbers/variables that are [added/multiplied/divided] and do not apply to any other property then it is substitution; you are substituting two numbers and an operation to a simplified value

### Example;

if you have the equation 5x+(3·4)=62 and you multiply 3 and 4 you get 12, so you substitute it into the equation and it is now 5x+12=62

### Example;

so applying the property to this equation [5(x+9)] you get this result; 5(x+9)=(5·x)+(5·9) which simplifies to 5x+45

### Communtative Property of Addition

when using addition throughout the whole equation, changing the order of the numbers does not affect the value of the sum; a+b+c=b+a+c

### Communtative Property of Multiplication

when using multiplication throughout the whole equation, changing the order of the numbers does not affect the value of the product; a·b·c=b·a·c

### Associative Property of Addition

when using addition throughout the whole equation, changing the grouping does not affect the value of the sum; (a+b)+c=a+(b+c)

### Associative Property of Multiplication

when using multiplication throughout the whole equation, changing the grouping does not affect the value of the product; (a·b)c=a(b·c)