To solve this, you need to cross multiply the fractions.
Let’s say you have these fractions:
A / B = C / D
To cross multiply, multiply the denominator of the first fraction (B) by the numerator of the second fraction (C). Multiply the numerator of the first fraction (A) by the denominator of the second fraction (D).
You get B x C = A x D
After cross multiplying your fractions, you get 63 = 7(c +4)
Distributing the 7 into c+4 gives you this:
63 = 7c + 28
Now solve this like a normal equation with a variable
63 = 7c + 28
35 = 7c
5 = c
To double check that, plug c = 5 into the original equation.
1/(5) + 4 = 7/63
1/9 = 7/63
7/63 simplifies into 1/9 (7:7 = 1, 63/7 = 9)
1/9 = 1/9 so c = 5 is correct