The given function is an absolute value function. For f(x) = 4, it means that
(4 - 7x)/7 = 4 or (4 - 7x)/7 = - 4
Multiplying the right hand side by 7, we have
4 - 7x = 28 or 4 - 7x = - 28
7x = 4 - 28 or 7x = 4 + 28
7x = - 24 or 7x = 32
x = - 24/7 or x = 32/7
The required values of x are
x = - 24/7 and x = 32/7