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In the world of Real Number there are 14 properties
each one relates to its own rules and is used when proofing an equation
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
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
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
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
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
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
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
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
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)
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