Complete the following stepped-out solution to show that −7+[(8⋅m)⋅18]+7 is equivalent to m. (2 points)
−7+7+[(8⋅m)⋅1/8] Commutative Property of Addition
0+[(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)⋅18]+7
Using the Commutative Property of Addition, we can rearrange the equation:
-7+7+[(8⋅m)⋅18]
Simplifying the middle terms using the Inverse Property of Addition (-7+7=0):
0+[(8⋅m)⋅18]
Simplifying the equation further using the Identity Property of Addition (0+a=a):
[(8⋅m)⋅18]
Using the Associative Property of Multiplication, we can rearrange the equation:
(8⋅18)⋅m
Simplifying (8⋅18=144):
144⋅m
Simplifying further using the Inverse Property of Multiplication (a/1=a):
(144⋅1/8)⋅m
Simplifying (144⋅1/8=18):
18⋅m
Finally, using the Identity Property of Multiplication (a⋅1=a):
m