Given the equation:
$$\frac{x - 1}{4 x - 1} = \frac{5}{2}$$
Multiply the equation sides by the denominator -1 + 4*x
we get:
$$x - 1 = 10 x - \frac{5}{2}$$
Move free summands (without x)
from left part to right part, we given:
$$x = 10 x - \frac{3}{2}$$
Move the summands with the unknown x
from the right part to the left part:
$$\left(-9\right) x = - \frac{3}{2}$$
Divide both parts of the equation by -9
x = -3/2 / (-9)
We get the answer: x = 1/6