Given the linear equation:
(34/5)-(13/10)*x = (3/5)*x-(27/10)
Expand brackets in the left part
34/5-13/10x = (3/5)*x-(27/10)
Expand brackets in the right part
34/5-13/10x = 3/5x-27/10
Move free summands (without x)
from left part to right part, we given:
$$- \frac{13 x}{10} = \frac{3 x}{5} - \frac{19}{2}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{\left(-19\right) x}{10} = - \frac{19}{2}$$
Divide both parts of the equation by -19/10
x = -19/2 / (-19/10)
We get the answer: x = 5