SOLUTION: It has been 7 years since my last algebra class. The answer is 8 but I am not sure how to solve this problem can you please help me : 2/3(x+6)=1+ (4x-7)/3 I have tried common de

Click here to see ALL problems on Linear-equations

Question 24045: It has been 7 years since my last algebra class. The answer is 8 but I am not sure how to solve this problem can you please help me :
2/3(x+6)=1+ (4x-7)/3
I have tried common denominator of 6
4(x+6)= 1+2(4x-7)
4x+24=1+8x-14
4x+24=8x-13
stuck here
I tried 3 as common denominator also
3(x+6)= 1+3(4x-7)
3x+18 = 16x-28
-13x=-46
stuck here
Found 2 solutions by rapaljer, PeterC:
Answer by rapaljer(4671) (Show Source):
You can put this solution on YOUR website!
Your mistake is that in both of your solutions, you forgot to multiply the 1 on the right side of the equation by the common denominator. This is what it should have been:

2/3(x+6)=1+ (4x-7)/3
I have tried common denominator of 6
4(x+6)= 6+2(4x-7)
4x+24=6+8x-14
4x+24=8x-8
32 = 4x
x=8

In your second solution, there were a couple of other errors to clean up. See if this looks better?

I tried 3 as common denominator also
2(x+6)= 3+(4x-7)
2x+12 = 4x -4
16 = 2x
x=8

R^2 at SCC

Answer by PeterC(8) (Show Source):
You can put this solution on YOUR website!
I am glad to see that you have tried to solve the problem yourself before asking for help. The problem with your solution is that you need to multiply both terms in the right-hand part by the common factor. That is, after multiplying by 6, you should have:

Actually, I would have multiplied by 3, the common factor in all of the denominators: