I have the following problem (see picture). The mass of $A$ is 3kg and the mass of $B$ is 2kg. I am told the pulley is not smooth and the difference in tension on either side $\Delta T$ is given by $$\Delta T = 3 + 0.3a$$ where $a$ is the acceleration of the two particles.
Now I am unsure why the tension on the left has to be bigger. The reason given in the book is that $A$ is more massive. However, if I do the calculation supposing that the tension of the right is greater, I have $$A : 3g - T = 3a$$$$B : T+ 3 + 0.3a - 2g = 2a$$ and combining these I find $a=2.78$ m/s$^2$. This is different to the answer of 1.26 m/s$^2$ we get if we presume the tension on the left is greater. But why do I even get an answer?
This is part of a bigger issue I am having, as I am trying to apply a similar approach to considering the problem of two masses, one on a table, and one hanging freely, both connected by a string that passes over a non-smooth pulley. However, again, I am not sure on which side of the string the tension will be greatest.