So how should I approach this question...
I get a result that's 10x more than the actual answer :/
As we are told the system is moving left, let left be positive. Let the tension in the left rope be
and the tension in the right rope be
.
Draw the forces the acting on each block.
For M1: mg is down and T1 is up
For M2: mg is down, N is up, T1 is left, T2 is right, friction is right (as we are told block is moving to the left)
For M3: mg is down, T2 is up
Since acceleration of whole system is the same, we can apply Newton's second law to each block individually.
For M1:
--- Eq. 1
For M2:
You also know that
Thus:
--- Eq. 2
For M3:
--- Eq. 3
Adding Eq. 1 and Eq 3. gives:
--- Eq. 4
Adding Eq. 2 and Eq 4. gives:
[EDIT: Whoops, got the fraction the wrong way around the first time]
(negative sign shows that it's decelerating)
Hope that helps.