/sci/ - Science & Math

I checked on my elementary high school math skills and I can't wrap my head around it. For an example:

17-2p=2p+5+2p

Combine like terms

17-2p = 4p + 5

Subtract -4

17 - 6p = 5

Subtract 17

-6p = -12

Divide by -6

p= -2

But when you are trying to get rid of the numbers, how do you know you have to subtract -4 to get rid of the 2p + 2p on the right side, and not get rid of the -2p on the left side?

Like:

17-2p=2p+5+2p

Add +2p and also subtract -5 to get rid of the 5 on the right side

12 = 4p + 4p

12 = 8p

8p = 12

12/8 = 1.5

p = 1.5

Is the only way to know this is wrong to manually enter it into the equation to check it, I thought there is a logic you can follow to do it right the first time.