Kirchoff's Rule - circuit with 3 batteries

[brazen2]

Homework Statement

Hello everyone

I need to find the current through the 22 ohm resistor. I've tried to solve this problem for many hours now... I can't find what I'm doing wrong! Please find a rough diagram attached.

Homework Equations

Kirchoffs rules

The Attempt at a Solution

I1 + I2 = I3

top loop:

-8 -22I1+12-14I3 = 0
0.286 - 1.57I1 = I3

perimeter loop:
-8 -22I1 +12 I2 -18 =0
2.17 +1.83 I1 = I2

Inputting these numbers into the first equation:
I1+I2=I3
I1 +2.17 +1.83I1 = 0.286-1.57I1
I1 = -0.428A

I then put the I1 into the loop equations and found:
I2= 1.39 A
I3= 0.958 A

However, when I'm trying to find the voltage across the points A and B, these currents do not yield consistent voltage drops across the three portions of the circuit.

I really appreciate any help!

 

[brazen2]

Sorry- i actually think this is correct. There goes a couple hours!