combining like terms in a linear equation.

[kimkiunke]

I can't seem to finish this problem. I'm fine until the combining like terms on each side. Is there a set of rules like if one of the terms is on the opposite side of the = then you subtract?? There doesn't seem to be a pattern to follow to get the right answer:

-7(y+1) =4y-6+2(2y+4)
-7y-7+4y-6+4y+8
-7y-7=8y+2
-7y=8y+9

I get all of this so far. Here is where I have trouble. Is there a set pattern to this? Because I never seem to get the write answer using the same formula:
-15y=9 I guess it's -7y+8Y and you get -15? How is that? If I add -7+8 I get 1 not -15. It looks like it's just 7+8 but how does it stay negative and how do I know that when solving? Example, what if it was 7y= -8Y? Would it still be -15? SO frustrating! I get everything but this part.

[jg.allinsymbols]

I can't seem to finish this problem. I'm fine until the combining like terms on each side. Is there a set of rules like if one of the terms is on the opposite side of the = then you subtract?? There doesn't seem to be a pattern to follow to get the right answer:

-7(y+1) =4y-6+2(2y+4)
-7y-7+4y-6+4y+8
-7y-7=8y+2
-7y=8y+9

I get all of this so far. Here is where I have trouble. Is there a set pattern to this? Because I never seem to get the write answer using the same formula:
-15y=9 I guess it's -7y+8Y and you get -15? How is that? If I add -7+8 I get 1 not -15. It looks like it's just 7+8 but how does it stay negative and how do I know that when solving? Example, what if it was 7y= -8Y? Would it still be -15? SO frustrating! I get everything but this part.

Sure, the rule is properties of equality. You do the same thing to both sides of the equation. What is stopping you from adding the additive inverse of 8y to both sides? Then you have something to combine.

[maggiemagnet]

Comment: Thank you for showing your steps and thinking so clearly!

-7y=8y+9

I get all of this so far. Here is where I have trouble....
-15y=9 I guess it's -7y+8Y and you get -15?

Not quite. You have to subtract the 8y from both sides to move it from the right to the left. You can see worked examples here.