Purple Math Simplification Problem

[freemathhelpuser]

I am trying to understand some logic behind a particular set of steps mentioned on Purplemath (below) on how to simplify parenthesis. http://www.purplemath.com/modules/simparen2.htm Simplify 9 – 3[x – (3x + 2)] + 4 I won't do anything with the "9 –" or the "+ 4" until I simplify inside the brackets and parentheses. I'll work from the inside out:

9 – 3[x – (3x + 2)] + 4
= 9 – 3[x – 1(3x + 2)] + 4
= 9 – 3[x – 1(3x) – 1(2)] + 4
= 9 – 3[x – 3x – 2] + 4
= 9 – 3[–2x – 2] + 4
= 9 – 3[–2x] – 3[–2] + 4
= 9 + 6x + 6 + 4
= 6x + 19

My issue is with the phrase: I won't do anything with the "9 –" or the "+ 4" until I simplify inside the brackets and parentheses. Why did they assume it was "9-"? It seems that they should have assumed it was "-3" and multiplied "-3" through the parenthesis.
Also, I tried to make it neater, but it appears the system won't let people start new lines of text at will. [edited]

 

[lookagain]

My issue is with the phrase: I won't do anything with the "9 –" or the "+ 4" until I simplify inside the brackets and parentheses.

Why did they assume it was "9-"?

It seems that they should have assumed it was "-3" and multiplied "-3" through the parenthesis.

It can be thought of in at least two ways:

"Nine minus the product of three and that expression"

"Nine plus the product of negative three and that expression"