HELP HELP HELP! I Don't Have A Clue How To Simplify This Expression For A Paper I Had To Do Over? Can You Explain? 3(k - 9) + K - 1

The order of operations says you deal with parentheses first.
k - 9 cannot be simplified, so you move on.

Next after parentheses is multiplication and division. Working from left to right, we find the first multiplication that is indicated is
3(k - 9)

The distributive property of multiplication over addition says we can write an equivalent form for this. At this point, you can decide how you want to treat the minus sign. You can attach it to the 9, or leave it separate. Let's leave it separate for now.
3(k - 9) = 3(k) - 3(9) = 3k - 27

Alternatively, we could keep the minus sign with the 9, like this
3(k - 9) = 3(k + (-9)) = 3(k) + 3(-9) = 3k + (-27) = 3k - 27

Having done the multiplication, our entire expression looks like this ...
3k - 27 + k - 1

Here is where your rule about the invisible 1 comes into play. We can look at this as though we have
3k - 27 + 1k - 1

Now, we "collect terms". That is, we put things involving k together, and things not involving k together.
3k + 1k - 27 - 1

For the terms involving k, we can use the distributive property in reverse. We can factor the k out all of the terms involving k, and write the sum of them as this ...
3k + 1k = k(3 + 1) = k(4) = 4k

Then, our entire expression becomes
3k + 1k - 27 - 1 = 4k - 27 - 1.

We can add the constants to complete the simplification. We know that if we subtract 27, then subtract 1 more, we have subtracted a total of 28:
4k - 27 - 1 = 4k - 28

Your simplification then looks like
3(k - 9) + k - 1
  = 3k - 27 + k - 1
  = 3k + 1k - 27 - 1
  = k(3+1) - 28
  = 4k - 28    (this is the simplified form)

Under some circumstances, it is helpful to factor 4 out of the expression, writing it like this ...
  = 4(k - 7)

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