Complete the following stepped-out solution to show that −7+[(8⋅m)⋅1/8]+7 is equivalent to m. (2 points)
−7+
+[(8⋅m)⋅1/8] Commutative Property of Addition
+[(8⋅m)⋅1/8] Inverse Property of Addition
(8⋅m)⋅1/8 Identity Property of Addition
(8⋅
)⋅ m Associative Property of Multiplication
(
)⋅m Inverse Property of Multiplication
m Identity Property of Multiplication
−7+[(8⋅m)⋅1/8]+7
Commutative Property of Addition: Rearrange the terms in any order without changing the value.
= -7 + 7 + [(8⋅m)⋅1/8]
Inverse Property of Addition: The sum of a number and its additive inverse is zero.
= 0 + [(8⋅m)⋅1/8]
Identity Property of Addition: The sum of any number and zero is the number itself.
= [(8⋅m)⋅1/8]
Identity Property of Multiplication: Any number multiplied by 1 is the number itself.
= (8⋅m)⋅1/8
Associative Property of Multiplication: The product of three or more numbers is the same regardless of how they are grouped.
= 8⋅(m⋅1/8)
Inverse Property of Multiplication: The product of a number and its multiplicative inverse is 1.
= 8⋅1⋅m
Identity Property of Multiplication: Any number multiplied by 1 is the number itself.
= 8⋅m
Therefore, −7+[(8⋅m)⋅1/8]+7 is equivalent to m.