If we know that f (x) is a linear function and satisfies 3f (x + 1) - 2F (x-1) = 2x + 17, then f (x) =? Each step should be described in detail,

If we know that f (x) is a linear function and satisfies 3f (x + 1) - 2F (x-1) = 2x + 17, then f (x) =? Each step should be described in detail,

Let f (x) = KX + B, then
f(x+1)=k(x+1)+b=kx+k+b
3f(x+1)=3kx+3k+3b
f(x-1)=k(x-1)+b=kx-k+b
2f(x-1)=2kx-2k+2b
3f(x+1)-2f(x-1)=(3kx+3k+3b)-(2kx-2k+2b)
=3kx+3k+3b-2kx+2k-2b
=kx+5k+b
∵3f(x+1)-2f(x-1)=2x+17
∴kx+5k+b=2x+17
∴k=2
5k+b=17
∴k=2,b=7
∴f(x)=2x+7