Proving equivelance of a multijump turing machine and a turing machine

I'm having trouble getting started on this proof, and I was hoping you guys could give me a couple hints/point me in the direction of where to start? Here's the problem:

Consider a multijump Turing machine, which is like an ordinary Turing machine except the transition function is δ : Q × Γ → Q × Γ × {LL, L, R, RR} In other words, the multijump TM can move left or right either one or two times. Show that a language can be recognized by a multijump TM if and only if it can be recognized by a TM.

I'm trying to answer it formally in terms of the 7-tuple and show that the TM and multijump TM are equivelant, but I'm having trouble getting started on that.

Any and all tips are appreciated, thanks

• What have you tried and where, specifically, did you get stuck? Have you read similar simulation proofs, e.g. for multi-tape vs single-tape or one-sided-infinite tape vs double-sided-infinte tape? – Raphael Nov 6 '14 at 15:26