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
= −7 + [(8 ⋅ m) ⋅ 1/8] + 7 (Commutive Property of Addition)
= (-7 + 7) + [(8 ⋅ m) ⋅ 1/8] (Associative Property of Addition)
= 0 + [(8 ⋅ m) ⋅ 1/8] (Inverse Property of Addition)
= [(8 ⋅ m) ⋅ 1/8] (Identity Property of Addition)
= (8 ⋅ m) ⋅ 1/8 (LHS: Identity Property of Multiplication)
= 8 ⋅ (m ⋅ 1/8) (Associative Property of Multiplication)
= 8 ⋅ (m/8) (Identity Property of Multiplication)
= (8/1) ⋅ (m/8) (Identity Property of Multiplication)
= (8 ⋅ m) / (1 ⋅ 8) (Division Property of Equality)
= (8 ⋅ m) / 8 (Identity Property of Multiplication)
= m (Inverse Property of Multiplication)
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
= −7 + [(8 ⋅ m) ⋅ 1/8] + 7 (Commutive Property of Addition)
= (-7 + 7) + [(8 ⋅ m) ⋅ 1/8] (Associative Property of Addition)
= 0 + [(8 ⋅ m) ⋅ 1/8] (Inverse Property of Addition)
= [(8 ⋅ m) ⋅ 1/8] (Identity Property of Addition)
= (8 ⋅ m) ⋅ 1/8 (Associative Property of Multiplication)
= 8 ⋅ (m ⋅ 1/8) (Associative Property of Multiplication)
= 8 ⋅ (m/8) (Identity Property of Multiplication)
= (8/1) ⋅ (m/8) (Identity Property of Multiplication)
= (8 ⋅ m) / (1 ⋅ 8) (Division Property of Equality)
= (8 ⋅ m) / 8 (Identity Property of Multiplication)
= m (Inverse Property of Multiplication)