Question

HELPPPPPP this is due tonight!!!!

Answer 1

(1) Commutative property

(2) Distributive property/Definition of addition

(3) Compatibility with addition/Existence of additive inverse/Modulative property

(4) Compatibility with multiplication/Associative property/Definition of division/Existence of additive inverse/Commutative and modulative properties/Result

Explanation:

We proceed to solve algebraically and explain each step:

1)
`4\cdot x +1 +x + 3 = -11` GIven

2)
`4\cdot x +x +1 + 3 = -11` Commutative property

3)
`(4+1)\cdot x +4 = -11` Distributive property/Definition of addition

4)
`5\cdot x +4 = -11` Definition of addition

5)
`5\cdot x +4 -4 = -11-4` Compatibility with addition

6)
`5\cdot x = -15` Existence of additive inverse/Modulative property

7)
`(1)/(5)\cdot (5\cdot x)= (1)/(5)\cdot (-15)` Compatibility with multiplication

8)
`x = - 3` Associative property/Definition of division/Existence of additive inverse/Commutative and modulative properties/Result

Hence, we have the following answers:

(1) Commutative property

(2) Distributive property/Definition of addition

(3) Compatibility with addition/Existence of additive inverse/Modulative property

(4) Compatibility with multiplication/Associative property/Definition of division/Existence of additive inverse/Commutative and modulative properties/Result