To solve this equation, we can start by simplifying both sides of the equation.

3/4 - (x - 4) - 1/7(x + 7) = 1/5x

First, let's simplify the expression inside the parentheses on the left side:

3/4 - x + 4 - 1/7(x + 7) = 1/5x

Next, distribute the -1/7 to both terms inside the parentheses:

3/4 - x + 4 - (1/7)x - (1/7)(7) = 1/5x

Simplify further:

3/4 - x + 4 - (1/7)x - 1 = 1/5x

Combine like terms:

7/4 - x - (1/7)x - 1 = 1/5x

To get rid of the fractions, we can multiply both sides of the equation by the least common denominator (LCD), which is 140:

140(7/4) - 140x - 140(1/7)x - 140(1) = 140(1/5)x

Simplify:

245/4 - 140x - 20x - 140 = 28x

Combine like terms:

245/4 - 160x - 140 = 28x

To isolate the variable, we can add 160x to both sides:

245/4 - 140 = 28x + 160x

Simplify:

245/4 - 140 = 188x

Multiply both sides by 4 to get rid of the fraction:

245 - 560 = 752x

Combine like terms:

-315 = 752x

Divide both sides by 752:

-315/752 = x

Therefore, the solution to the equation is x = -315/752.