Question

Identifying the Property of Equality

Quick

Check

Identify the correct property of equality to solve each equation.

3+x= 27

X/6 = 5

Answer 1

3 + x = 27

✔ subtraction property of equality with 3

x over 6 = 5

✔ multiplication property of equality with 6

Answer 2

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

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)
`(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