Split multisource circuit into smaller, simpler circuits, compute current or voltage and add.
Pick one source, turn off all or set to zero all others:
- Set Voltage Sources to V=0, doesn't care about current so is a short
- Set Current Sources to I=0, doesn't care about the voltage so turns into an open
Find the current through the 3 ohm resistor assuming moving left to right is positive:
The total current in the direction shown on the original diagram is going to be:
Find the current through the 4 ohm resistor assuming moving left to right is positive:
Simulation at circuit lab confirms the answer: