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.
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