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
Using the Commutative Property of Addition, we can rearrange the terms:
−7+7+[(8⋅m)⋅1/8]
7 and -7 are additive inverses, so their sum is 0:
0+[(8⋅m)⋅1/8]
Using the Identity Property of Addition, we can eliminate the 0:
[(8⋅m)⋅1/8]
Using the Associative Property of Multiplication, we can rearrange the terms:
[(1/8)⋅(8⋅m)]
Using the Inverse Property of Multiplication, we can simplify:
[(1/8)⋅(8⋅m)] = 1⋅m = m
Finally, using the Identity Property of Multiplication, we can eliminate the unnecessary 1:
m