I need help on justify each step.

5(n+4)+9n=(5+20)+9n
=5n+(20+9n)
=5n+(9n+20)
=(5n+9n)+20
=(5+9)n+20
=14n+20

PLease and Thank-You

5(n+4)+9n
=(5n+20)+9n distribution
=5n+(20+9n) addition
=5n+(9n+20) addition
=(5n+9n)+20 addition
=(5+9)n+20 factoring
=14n+20 order of operations

I don't think you're using the distributive propery correctly. That property states:
a(b+c)=a*b + a*c
So 5(n+4)=5n+20
I performed the arithmetic at the same time I distributed, but the expression could also be
5(n+4)=5n+5*4

Here is a possible sequence of steps to simplify the given expression.
Statement Reason
_____________________
5(n+4)+9n Given
=5n+20+9n Distributive property, arithmetic
=5n+9n+20 Commutative property
=(5n+9n)+20 Associative property
=(5+9)n+20 Distributive property
=14n + 20 Arithmetic

A couple things should be pointed out here. In the second step I could've write 5(n+4)=5(n)+5(4). The parentheses on the right hand side are really unnecessary because we usually reserve parentheses for expressions with two or more terms. In the third step no parentheses are needed at all. I notice in your 2nd step you used parentheses, but they're not needed (at least in my opinion they aren't). We can have any number of terms and nnd no parentheses at all.
In my 3rd step I inserted parentheses because the associative property also says that operations performed at the same level of precedence can be done in any order, i.e. parentheses can be inserted in any meaningful manner.
You also should be aware that the distributive property works on both the left and the right, thus a(b+c)=(b+c)a. Be aware of equivalent expressions for the distributive too: ab+ac=a(b+c) and ab+ac=ba+ca=(b+c)a. These are all equivalent ways to state the distributive property.
Finally, there is usually more than one correct way to simplify an expression. So don't think there is just 'the one and only correct ansswer', there isn't generally only one set of steps. Just make sure you used the correct property at each line.
One last word, take your teacher's instruction as the final word on the subject for now, not mine.

HOW DO YOU SIMPLIFY 5 OVER 5 SQUARE ROOT OF 2??

54n

by dividing 5 into 5 and it equals 1 with a square root of 2 and that equals 1.

To simplify the expression 5/(5√2), you can multiply the numerator and denominator by the conjugate of the denominator. The conjugate of √2 is -√2.

Step 1: Multiply the numerator and denominator by the conjugate of the denominator (-√2).

5/(5√2) * (-√2)/(-√2)
= -5√2 / (-5 * √2 * √2)
= -5√2 / (-5 * 2)
= -5√2 / -10
= 1/√2

So, the simplified form of 5/(5√2) is 1/√2.

To simplify 5 divided by the square root of 2, you can rationalize the denominator. The square root of 2 can be written as √2. To rationalize the denominator, you multiply the numerator and denominator by the conjugate of the denominator.

The conjugate of √2 is -√2 (since multiplying a negative by a positive yields a negative). So, multiply the numerator and denominator by -√2:

(5 * -√2) / (√2 * -√2)

Simplifying this expression, you get:

-5√2 / (-2)

Dividing both numerator and denominator by -1 to simplify the negative sign, you have:

5√2 / 2

Therefore, the simplified form of 5 divided by the square root of 2 is 5√2 / 2.