[CindyDawg]

Yep. Thanks.I'm gonna get me a "math for dummies" I hate algebra.

2x-(x+6(x-3))+y

2x-(x+6(x)+6(-3))+y (got that)

2x-(x+6x-18)+y (the 18 - because you have a positive and neg?)

2x-(7x-18)+y (got that)

2x +(-1)(7x)+(-1)(-18)+y (why did it change to plus behind the 2x and it doesn't look like it affects the answer but where did the (-1)s come from?

2x-7x+18+y=-5+y+18 (why -5 instead of 5?)

[Beaker]

Hi!
Sorry I didn't get back to you last night. I'm trying to get over a killer cold.

So your equation is 2x-(x+6(x-3))+y

I assume that you want to solve for x and y, so to do that you set the equation to zero.

2x-(x+6(x-3))+y = 0

So! The first rule of solving equations like these is the acronym PEMDAS. It tells you what operations to do in what order. So P=Parenthesis. E=Exponents M=Multiplication D=Distribution A= Addition S=Subtraction.

So we look at the parenthesis and see that we can't do much with them yet. There are no exponents, so scratch that. But, we can mulitply the 6 through the (x-3). You multiply the x and the 3 by 6 because they are in parenthesis. (You did this correctly.)

Multiplying 6(x-3) you get:
2x-(x+6x-18)+y=0

Now we have a whole "new" equation to look at, so we have to look at our acronym again. So, the first step is Parenthesis and look! There is stuff in the parenthesis to work with! hooray! Adding the x's together, that symplifies the equation down to:

2x-(7x-18)+y=0

Now we have to get rid of the parenthesis. To do that you have to distribute out the subtraction symbol in front, (which is the same as putting a -1 in front) to the stuff that's in parenthesis. You do nothing to the y because the y isn't in parenthesis. In your equation, they stick in the negative 1s because it reminds you to keep things negative and positive. It's confusing because it's like they pulled numbers out of thin air. But if we were to think of the subtraction sign as a negative 1, the equation would look like this:

2x-1(7x-18)+y=0

2x-1 is the same as 2x+(-1). I put the -1 in parenthesis to make it easier to read.
So the equation looks like this 2x+(-1)(7x-18)+y =0 Multiplying the -1 through the stuff in the parenthesis, the equation becomes:

2x-7x+18+y=0
The 7 is negative because the 1 is negative, and the 18 is positive because a neg. and a neg. is a positive. (-1 and -18)

Adding the 2x and -7x you get:

-5x+18+y=0

As to why the 5 is neg:
Whenever you add a smaller positive number to a larger negative number, the sign (pos. or neg.) of the number is going to be negative.

If it was something like -5-7, the answer would be -12, because you're adding two negative numbers. (-5+-7).

Now we get to solve the equation for x and y.

Our equation is:
-5x+18+y=0

To solve for a variable, you have to get it by itself. First we want to solve for y because it's the easiest. To to that, we have to move -5x and 18 over to the other side of the equation so that y is by itself. When you move numbers over to the other side of the equation, their signs change. So we get:

y = 5x-18

We now have to get rid of the x. 5x is just like 5*x. Subsitute in 0 for x, and 5*0=0. In other words, no x. So the equation looks like:

y = 0-18. y = -18. We've just solved for y.

Now, going back to our simplified equation -5x+18+y=0, we're going to solve for x. We do for y, what we did for 5x. Substitute 0 for y and get rid of it so that we get:

-5x+18+0=0
Solving for x: -5x=-18

x=18/5. (2 neg. = positive when you're dividing or multiplying)