If L is decidable, then the language $L^R$ = {$w^R$|w ∈ L} of the reversals of all strings in L is decidable too.
My approach to this was to define M' as a decider for $L^R$ such that it was a modified version of M. M' would reverse all transitions of M such that the direction is the reverse (by swapping the defined states in the transition around) and swap the initial state with the halting state ha around
Would this not be a solution that shows that $L^R$ is also decidable?
I know the alternative is to construct a compiler that takes input $w^R$ and reverses it to $w$. Feed w$ in to M and if M accepts then M' accepts etc.