Question

HELPPPPPP this is due tonight!!!!

Answer 1

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) $4\cdot x +1 +x + 3 = -11$ 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) $\frac{1}{5}\cdot (5\cdot x)= \frac{1}{5}\cdot (-15)$ 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