Engineering Is my answer correct? (Mesh Currents)

[REEEEEEEE]

Homework Statement

a) Determine the power
dissipated in resistor R6 using
one of the systematic methods to your
choice (nodes method or method
of the meshes). I chose mesh

Data:

Circuit data:
R1 = 2kohm; R2 = 4kohm; R3 = 2kohm;
R4 = 5kohm; R5 = 1kohm; R6 = 3kohm;
V1 = 30V; V2 = 10V; IS = 10mA

Relevant Equations

p=I^2*R
V=RI

Hello I am solving the following circuit bellow on the homework statement terms I will leave also my resolution as a png And appologise in advance i my writing is hard to read

My solution:

Can you tell me if I am on the right track or help me get there?
Your help time and attention are deeply appreciated .
Thank you.

 

[lewando]

The image is unreadable in the center area. You are going to need to fix that. I can make out that you are claiming that I₂ is -10 mA. Why is it negative?

 

[DaveE]

I got a different value, based on different methods. Then I checked to see if I was correct (see below), because we all make mistakes.

I haven't checked your work because it's not worth the effort. If you want volunteers to help you, try harder to do the work you can do yourself. I'll comment on circuit analysis, but I won't do the image editing instead of you.

Also, if you ever intend to work in STEM fields, you need to learn not just to solve problems, but also to check your work. Now that you think you know some of the circuit values, write them down on the schematic and work the problem backwards. Do the currents all cancel at the nodes (like KCL says), do the voltages around the loops all sum to zero (like KVL)?