alright, so once again I've confused myself. This time about the meaning of something as simple as "minus/negative". I have multiple questions, so answer what you can.
Question 1) So as I saw it before was that when I have, say $5-4x$, or just $-4x$ it would mean the exact same (in regards to the $-4x$): "minus four, times x", but Ive come to realize today that apparently one should interpret $5-4x$ as: "five, minus, four times x)" aka basically $5-(4×x)$. Which one is it?
Question 2 which basically expands on question 1) The idea of "adding a negative". It is obvious to me that $5+(-3)=5-3=2$ since the 3 definitely is "negative". However, $5+(-5×3)$ or $5+(-x×y)$ ?? What should I think about the $-5×3$ or the $-x×y$? Adding a negative is negative, but are we really adding a "negative"? Because as I see it now, it is just minus x, times y, and minus 5, times 3. That is to ask, why is $+(-x×y)=-x×y$.
Let me make this question clearer. Let's have a term with a minus negative variable inside, but let's not simplify the term: $$5+(-x×(-y)$$ You see, to simplify this, should one think of the latter term as $-(x×(-y)$? Can you do that, and is it the same thing? My books and the internet tell me to keep the sign negative WHENEVER a plus is followed by a minus,and change to positive WHENEVER 2 negatives come after each other. Is it best to just accept this rule? Why does it work? For example $+(-a×5×4×f×(-c))$ simplifies to (not opening the (-c)) $-a×5×4×f×(-c))$ based purely on the logic that the sign immediately after the + is minus. conversely $-(-a×5×4×f×(-c))$ simplifies to $-a×5×4×f×(-c))$ on the logic that "the sign after the minus is a minus"
question 3) Somewhat related as well. For as long as I've done algebra, and when I've had to open brackets (use the distributive property) or just multiply both sides of an equation, I've gone with this logic without realizing: Say I have $-5x(2-y+c)$ Then I multiply each term with the $-5x$ so I get $-10y, 5xy, -5cx$ and now I just look at the signs, 2 of them have minuses so I wont touch them, but since the $5xy$ doesn't have a sign I assume it means $+5xy$ just as 5 means +5. Then I place them next each other (basically add them?) and get $-10x+5xy-5cx$. Is this valid? It certainly has always given the right answer.
I'll try to respond if you don't understand my questions. Thank you in advance.