I actually don’t know how to begin in the first place. The first thought that went through mu head was to consider the 2kg and 3kg and the pulley as a singular system, but that isn’t possible because they’d have different accelerations. I could have written a constraint equation, but that isn’t right or very useful because there are three separate strings. Nonetheless here is the what I wrong (it’s probably wrong)
$a_1-2a_2-2a_3=0$
How should I i approach this question?
Let me write $m_{1}=1$ kg, $m_{2}=2$ kg and $m_{3}=3$ kg.If you draw the forces on each block, you will find the equations (I'm assuming the system is frictionless) $$m_{3}g - T_{1} = m_{3}a \hspace{1cm} (1) $$ $$T_{1}-m_{2}g=m_{2}a \hspace{1cm} (2)$$ and $$2T_{2} = T_{1} = m_{1}a \hspace{1cm} (3)$$ Equations (1) and (2) together become $$a = \frac{(m_{3}-m_{2})g}{m_{3}+m_{2}} \hspace{1cm} (4)$$ So you can solve it by substituting (4) into (3).