Simplifly variable Expressions

I need help on justify each step.

PLease and Thank-You

=(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

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.


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  1. 54n

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

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