Question

Identifying the Property of Equality

Answer 1

Answer:

3 + x = 27

✔ subtraction property of equality with 3

x over 6  = 5

✔ multiplication property of equality with 6

Answer 2

Answer:

a) Compatibility of Equality with Addition, b) Compatibility of Equality with Multiplication

Step-by-step explanation:

a) This expression can be solved by using the Compatibility of Equality with Addition, that is:

1) $3+x = 27$ Given

2) $x+3 = 27$ Commutative property

3) $(x + 3)+(-3) = 27 +(-3)$ Compatibility of Equality with Addition

4) $x + [3+(-3)] = 27+(-3)$ Associative property

5) $x + 0 = 27-3$ Existence of Additive Inverse/Definition of subtraction

6) $x=24$ Modulative property/Subtraction/Result.

b) This expression can be solved by using the Compatibility of Equality with Multiplication, that is:

1) $\frac{x}{6} = 5$ Given

2) $(6)^{-1}\cdot x = 5$ Definition of division

3) $6\cdot [(6)^{-1}\cdot x] = 5 \cdot 6$ Compatibility of Equality with Multiplication

4) $[6\cdot (6)^{-1}]\cdot x = 30$ Associative property

5) $1\cdot x = 30$ Existence of multiplicative inverse

6) $x = 30$ Modulative property/Result