Given the linear equation:
(x+3)/12-1*(x-3)/4 = (x+2)/6
Expand brackets in the left part
x/12+3/12-1*x/4+1*3/4 = (x+2)/6
Expand brackets in the right part
x/12+3/12-1*x/4+1*3/4 = x/6+2/6
Looking for similar summands in the left part:
1 - x/6 = x/6+2/6
Move free summands (without x)
from left part to right part, we given:
$$- \frac{x}{6} = \frac{x}{6} - \frac{2}{3}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{\left(-1\right) x}{3} = - \frac{2}{3}$$
Divide both parts of the equation by -1/3
x = -2/3 / (-1/3)
We get the answer: x = 2