Question 165267
This is not a geometric proof question.  This is an algebra proof question.

You were given:

5(x + 4) = 40

You now want to remove the parentheses by multiplying 5 by every terms inside the parentheses.

5(x + 4) becomes 5x + 20

The reason I was able to find 5x + 20 is called the distributive law or rule.

We now have this:

5x + 20 = 40....We now want to subtract 20 from both sides.  This is called the inverse of addition operation.  This is obtained from the subtraction property of equality.  

5x + 20 = 40

5x = 40 - 20

5x = 20

Here's what your final prove table looks like:

Given: 5(x + 4)= 40
Prove: x = 4 

Statements:

1. 5(x+4)= 40
2. 5x + 20 = 40
3. 5x = 20  
4. x = 4 

Reasons:

1.Given
2. Distributive law or rule
3. subtraction property of equality.
4. Substitution Property

I hope this helps.