Given the linear equation:
(3*x-2)/8 = (2*x+1)/3
Expand brackets in the left part
3*x/8-2/8 = (2*x+1)/3
Expand brackets in the right part
3*x/8-2/8 = 2*x/3+1/3
Move free summands (without x)
from left part to right part, we given:
$$\frac{3 x}{8} = \frac{2 x}{3} + \frac{7}{12}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{\left(-7\right) x}{24} = \frac{7}{12}$$
Divide both parts of the equation by -7/24
x = 7/12 / (-7/24)
We get the answer: x = -2