Solve (3x+6)/4 - (2x-6)/5 = (x+7)/8.

To solve this equation for x, we need to get x on its own. To do this, we first need to multiply through by the denominators of the fractions, as none of them contain an x term. Multiplying through by 8 first, we get 2(3x+6) - 8(2x-6)/5 = x+7. We then need to multiply through by 5 to get 10(3x+6) - 8(2x-6) = 5(x+7). Now there are no fractions. The next thing to do is to expan the brackets. We have 10(3x) + 10(6) - 8(2x) - 8(-6) = 5(x) + 5(7) which is the same as 30x + 60 - 16x + 48 = 5x + 35. We can now rearrange the equation to get x terms on the left, and constants on the right. 30x - 16x - 5x = 35 - 60 - 48 and we then simplify this to get 9x = -73. Finally, we can solve for x by diving through by 9, the coefficeint of x, to get x = -73/9 = -8 1/9.