Given the linear equation:
(k-3)/4 = (3*k-3)/11
Expand brackets in the left part
k/4-3/4 = (3*k-3)/11
Expand brackets in the right part
k/4-3/4 = 3*k/11-3/11
Move free summands (without k)
from left part to right part, we given:
$$\frac{k}{4} = \frac{3 k}{11} + \frac{21}{44}$$
Move the summands with the unknown k
from the right part to the left part:
$$- \frac{k}{44} = \frac{21}{44}$$
Divide both parts of the equation by -1/44
k = 21/44 / (-1/44)
We get the answer: k = -21