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Answer:

(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

Step-by-step explanation:

We proceed to solve algebraically and explain each step:

1) [tex]4\cdot x +1 +x + 3 = -11[/tex] GIven

2) [tex]4\cdot x +x +1 + 3 = -11[/tex] Commutative property

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

4) [tex]5\cdot x +4 = -11[/tex] Definition of addition

5) [tex]5\cdot x +4 -4 = -11-4[/tex] Compatibility with addition

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

7) [tex]\frac{1}{5}\cdot (5\cdot x)= \frac{1}{5}\cdot (-15)[/tex] Compatibility with multiplication

8) [tex]x = - 3[/tex] 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

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