Parentheses are very important things! In your post you wrote:

2/3(1/2-x+1/4)=5/6

which is:

The solution to this is indeed x = -1/2. But problem #51 is actually this:

which is entirely different. In your post you should have written it as:

2/3(1/2-(x+1)/4)=5/6

Note the extra set of parentheses! To solve this:

1. Multiply both sides by 3/2 to get: 1/2-(x+1)/4=5/6 x 3/2 = 5/4

2. Subtract 1/2 from both sides: -(x+1)/4 = 5/4 - 1/2 = 3/4.

3. Multiply both sides by 4: -(x+1) = 3/4 x 4 = 3

4. Multiply both sides by -1: x+1 = -3

5. Subtract 1 from both sides: x = -3-1 = -4.