Maximum power of circuit with dependent voltage source

[iharuyuki]

Homework Statement

Homework Equations

V(oc) = I(sc) * R(th)
Kirchoff's voltage law

The Attempt at a Solution

a) is okay. For part b):

After redrawing with the R(th) and V(th) found in part a):

Equations of loops:
s is I(sc)
a is I(left loop)

left loop:
-8 + a(4000) + (a-s)(4000) = 0

right loop:
(s-a)(4000) - (2000)x = 0

I(x):
a-s = x

I(sc) comes out to 0.2 mA
Then V(oc) = I(sc) R(th)
4 V = (0.002 A) R(th)
R(th) = 2 kOhm = R(L max)

However, this is 1 kOhm off from the answer.

What is the problem with the above working?

Thank you very much.

 

[iharuyuki]

All is good, thanks!