2z+5=5+2z
3-3x=3(1-x)
(8 9) b=8(9b)
a=1a
Which one are
Commutive property
Distributive property
Associative property
Identity property
The properties of equality used in the given equations are:
1) Commutative property - This property states that the order in which numbers are added or multiplied does not affect the result. In the equation 2z + 5 = 5 + 2z, the commutative property is being used because the order of the terms on both sides of the equation is being switched.
2) Distributive property - This property states that when a number is multiplied by a sum or difference inside parentheses, you can distribute the multiplication to each term inside the parentheses. In the equation 3 - 3x = 3(1 - x), the distributive property is being used because the number 3 is being multiplied by the expression inside the parentheses.
3) Identity property - This property states that when you add zero to a number, or multiply a number by one, the result is the original number. In the equation 8(9) * b = 8(9 * b), the identity property is being used because 9 is being multiplied by b, which does not change the value.
4) There is no associative property being used in the given equations. The associative property states that when adding or multiplying three or more numbers, the grouping of the terms does not affect the result. None of the equations involve adding or multiplying three or more numbers.
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The properties involved in each equation are as follows:
1) 2z + 5 = 5 + 2z: This equation involves the commutative property of addition.
2) 3 - 3x = 3(1 - x): This equation involves the distributive property.
3) (8 9) b = 8(9b): This equation does not involve any of the properties mentioned.
4) a = 1a: This equation involves the identity property.
Let's break down each equation and determine which property is being demonstrated.
1. 2z + 5 = 5 + 2z
This equation demonstrates the commutative property of addition. The commutative property states that the order of numbers in an addition operation does not affect the sum. Regardless of the order, the sum remains the same. In this case, the numbers 2z and 5 were swapped in the equation, but the result remains the same.
2. 3 - 3x = 3(1 - x)
This equation demonstrates the distributive property. The distributive property allows us to multiply a number by the sum (or difference) of two other numbers. In this case, we are distributing the 3 on the outside of the parentheses to both 1 and -x.
3. (8 9) b = 8(9b)
This equation does not demonstrate any of the given properties. Parentheses are usually used for grouping or indicating multiplication but in this case, it seems to be a typographical error rather than representing any mathematical property.
4. a = 1a
This equation demonstrates the identity property of multiplication. The identity property states that any number multiplied by 1 is equal to itself. In this case, the variable "a" is being multiplied by 1, and therefore remains unchanged.