Solving Fictitious Forces w/ Massless Pulley

[yngstr]

Homework Statement

All surfaces are frictionless, pulley is massless. What force, F is needed so that m3 does not rise or fall?

Picture attached

Homework Equations

F=ma

The Attempt at a Solution

Found acceleration of system by dividing F by all three masses.

Found Fictitious force felt by m2 as a result of the acceleration.

Equated this fictitious force with m3g, isolated F.

Just wanted to know if this is the right method towards solving this problem, or am I missing something obvious/big?

 

[Mindscrape]

Though you haven't posted any equations, your logic is alright.