Combining Like Terms & Distributive Properties

[munizz]

Here's one example of my delima:
4x - 3y - 2x - 4y The computer tells me the correct answer is: 2x - 7y...why was the 3y and the 4y added?
*so I take the 4x and the 2x and subtract
*Then I take the 3y and the 4y and subtract...or at least I thought.....
that's where I'm stumpped. What is the decding factor for adding or subtracting once you've put together the like terms? Then how do I put the answer all together, how do I decide if I use +'s or -'s between each answer.
Every time I thought I figured it out the computer put out an answer that subtracted two of the like terms when we thought we were supposed to add them or vice versa. Recap: I am unsure when to add or subtract once we find the like terms then we are unsure whether to put a + or - between the numbers in the answer as well as what terms come first in the answer: if i would have wrote 7y - 2x would that have been wrong? Thank you so very much for your time and help!!!!!!!!!!!

 

[BigGlenntheHeavy]

\(\displaystyle 4x-3y-2x-4y\)

. . .\(\displaystyle =[4x+(-2x)]+[(-3y)+(-4y)]\)

. . .\(\displaystyle =[2x(2-1)]+[y(-3-4)]\)

. . .\(\displaystyle =[2x(1)]+[y(-7)]= 2x-7y\)

 

[munizz]

\(\displaystyle 4x-3y-2x-4y\)

. . .\(\displaystyle =[4x+(-2x)]+[(-3y)+(-4y)]\)

. . .\(\displaystyle =[2x(2-1)]+[y(-3-4)]\)

. . .\(\displaystyle =[2x(1)]+[y(-7)]= 2x-7y\)

I greatly appreciate the response, the only thing is....the computer already is giving me the answers, my problem is I dont understand the concept. When to add when to subtract. What concept to go by as I explained in my question. I know how to put combing terms together but what decides whether you add or subtract and what decides what signs to use between the numbers you come up with in the answer. For example: the answer was 2x-7y....out of the original problem what made you decide to make it a minus between the 2x and the 7y and what made you decide to add the 3y to the 4y instead of subtracting like the problem indicates. Thank you once again.........greatly!!!

 

[Denis]

Here's one example of my delima: 4x - 3y - 2x - 4y
The computer tells me the correct answer is: 2x - 7y...why was the 3y and the 4y added?
*so I take the 4x and the 2x and subtract
*Then I take the 3y and the 4y and subtract...or at least I thought.....that's where I'm stumpped.

4x - 2x - 3y - 4y
= 2x - 3y - 4y
= 2x - (3y + 4y)
= 2x - 7y

You have $10, and spend $2 buying apples, then $3 buying bananas; you got 5 bucks left, right?
10 - 2 - 3
= 10 - (2+3)
= 10 - 5 = 5 bucks

Your problem is just as simple...