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Answer:

(1) commutative property of the addition.

(2) distributive property of the multiplication and associative property of the addition.

(3) addition property of the equality.

(4) multiplication property of the equality.

Step-by-step explanation:

First we start with:

4x + 1 + x + 3 = -11

Here we use the commutative property of the sum, which says that:

A + B = B + A

So we can reorder the terms in a sum, and we can rewrite our equation as:

4*x + x + 3 + 1 = -11

Here we also used the associative property of the sum, that says that:

A + B + C = (A + B) + C = A + ( B + C)

wich means that we can perform the sum in any order we want, then we can add the 3 and the 1

4*x + x + 4 = -11

Now we use the distributive property of the multiplication, which says that:

(A + B)*C = A*C + B*C

Then we can rewrite our equation as:

(4 + 1)*x + 4 = -11

Now we solve the sum in the parentheses to get:

5*x + 4 = -11

Now we can use the addition property of the equality, we can add (-4) in both sides to get:

5*x + 4 - 4 = -11  - 4

5*x = -15

Now we can use the multiplication property of the equality, and multiply both sides by (1/5) to get:

5*x*(1/5) = -15*(1/5)

x = -5

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