PDE: Find an explicit expression for the solution of the IVP by using Fourier Transform

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Find an explicit expression for the solution of the IVP:

$u_{t}+cu_{x}+u=0$

$u(0,x)=f(x)$

by using Fourier Transform

That's how I started but don't quite understand what to do after! Any help would be highly appreciated! Thank you enter image description here