Given the linear equation:
(x-4)/4 = (x+3)/7
Expand brackets in the left part
x/4-4/4 = (x+3)/7
Expand brackets in the right part
x/4-4/4 = x/7+3/7
Move free summands (without x)
from left part to right part, we given:
$$\frac{x}{4} = \frac{x}{7} + \frac{10}{7}$$
Move the summands with the unknown x
from the right part to the left part:
$$\frac{3 x}{28} = \frac{10}{7}$$
Divide both parts of the equation by 3/28
x = 10/7 / (3/28)
We get the answer: x = 40/3