Question

2f(x)+3f(-x)=15-4x. find f(x)

Answer 1

As RHS has highest degree 1, LHS too must have a polynomial of degree 1 (As they are equated in given question)

Let f(x) = ax+b
So that, f(-x) = -ax+b 

Placing them in given question 2f(x)+3f(-x)=15-4x.
2(ax+b)+3(-ax+b) = 15-4x
2ax+2b-3ax+3b = 15-4x

Equating coefficient of x      
2a-3a = -4
-a = -4
a=4

Equating constants
2b+3b=15
5b=15
b=3

therefore, f(x) = ax+b = 4x+3
f(x) = 4x+3 is the answer