To make c the subject of the formula v = 1 - \(\frac{a}{5}\)(b + \(\frac{3c}{7}\)), we can follow these steps:

1. Subtract 1 from both sides: v - 1 = -\(\frac{a}{5}\)(b + \(\frac{3c}{7}\))
2. Multiply both sides by -\(\frac{5}{a}\): -\(\frac{5}{a}\)(v - 1) = b + \(\frac{3c}{7}\)
3. Subtract b from both sides: -\(\frac{5}{a}\)(v - 1) - b = \(\frac{3c}{7}\)
4. Multiply both sides by \(\frac{7}{3}\): \(\frac{7}{3}\)(-\(\frac{5}{a}\)(v - 1) - b) = c

So, the expression for c in terms of a, b, and v is c = \(\frac{7}{3}\)(-\(\frac{5}{a}\)(v - 1) - b)