Question

Hi! please help. thank you!

Answer 1

Step 6 is done by Additive Property of Equality, also known as Compatibility of Equality with Addition, which is defined by the following expression:

`a = b \to a + c = b + c`,
`\forall\,a,b, c\,\in \,\mathbb{R}`

Explanation:

Step 6 is done by Additive Property of Equality, also known as Compatibility of Equality with Addition, which is defined by the following expression:

`a = b \to a + c = b + c`,
`\forall\,a,b, c\,\in \,\mathbb{R}`

1)
`(7\cdot x - 3) + 3 = (2\cdot x + 7) + 3` Associative property/Compatibility with addition

2)
`7\cdot x + [3 + (-3)] = 2\cdot x + (7 + 3)` Associative and commutative properties/Definition of subtraction

3)
`7\cdot x + 0 = 2\cdot x + 10` Existence of the additive inverse/Definition of addition

4)
`7\cdot x = 2\cdot x + 10` Modulative property/Result