Help Solving this equation

Question

1/3(x-5) + 5/6(x+1) = x-2

 

Here is where I got to, feel free to correct me if its all wrong

 

I distributed everything and got the following;

 

1/3x - 5/3 + 5/6x + 5/6 = x-2

 

Then I changed everything to have like signs

 

2/6x + 5/6x -10/6 + 5/6 = x-2

 

Once I started combining like terms I just ran into a big mess so I don't know if I was doing it right

 

Answer 1

So far so good, Steve.  To continue:

 

(2/6)x + (5/6)x - (10/6) + (5/6) = x - 2

 

(7/6)x - (5/6) = x - 2

 

(7/6)x - x = -2 + 5/6

 

(1/6)x = -7/6

 

x = -7

 

Check:

(1/3)(x-5) + (5/6)(x+1) = x - 2

(1/3)(-7-5) + (5/6)(-7+1) = -7 - 2

(1/3)(-12) + (5/6)(-6) = -9

-4 + -5 = -9

-9 = -9

Check!