Given the linear equation:
(x+3)/3 = (3-x)/8
Expand brackets in the left part
x/3+3/3 = (3-x)/8
Expand brackets in the right part
x/3+3/3 = 3/8-x/8
Move free summands (without x)
from left part to right part, we given:
$$\frac{x}{3} = - \frac{x}{8} - \frac{5}{8}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{11 x}{24} = - \frac{5}{8}$$
Divide both parts of the equation by 11/24
x = -5/8 / (11/24)
We get the answer: x = -15/11