Question

Help Please Given the equation 3x − 3 = 6x + 1, select the reasoning that correctly solves for x.


Add 3, subtract 3x, then divide by −3.
Add 3, subtract 6x, then divide by 3.
Subtract 1, subtract 3x, then divide by 3.
Subtract 1, subtract 6x, then divide by −3.

Answer 1

well A and D are definetly out, it can be either C or B

Answer 2

still need help

Answer 3

To complete this problem, you must keep in mind that what you do to one side, you must do to the other. To begin: 3x-3=6x+1. The order in which these are done can vary and you are trying to get all the like terms on one side. So, everything with an "x" on one side and everything without an "x" on the other.

I can subtract 1 from each side: 3x-4=6x.
I can then subtract 3x from each side: -4=3x.
I can then divide both sides by 3 (to isolate the "x", "3x" means 3 multiplied by "x"):
-(4/3)=x

Looking at the answers offered, if I follow the steps for each:
Answer 1: Add 3, subtract 3x, divide by -3
3x=6x+4
Whoops... if I now subtract 3x, I get nothing on the left, so that's not what you're after.

Answer 2: Add 3, subtract 6x, divide by 3
3x=6x+4
-3x=4
-x=4/3
I'd need to do one more step to get a true answer. Multiply both sides by -1.

Answer 3 follows the steps I used in the first example.

Answer 4: Subtract 1, Subtract 6x, divide by -3
3x-4=6x
Oh dear. If I subtract 6x now, I'm left with nothing on the right. This is the same problem we had with Answer 1.

I hope this helps explain not just the correct answer, but how you can arrive at it. Good luck!