[I'm still thinking sorry]
I'm assuming 2x-12 is the angle measure of DAC in degrees.
Let p=AB=AD, q=AC
By the Law of Cosines,
22² = p² + q² - 2pq cos 48°
q² - 2pq cos 48° + p² - 22² = 0
We also require by the triangle inequality
CD+AD < AC
16 + p < q
Let's set them equal and see where we are.
q=p+16
(p+16)² - 2p(p+16) cos 48° + p² - 22² = 0
p≈12.2125,
q≈28.2125
16² = p² + q² - 2 pq cos DAC
16² = 12.2125² + 28.2125² - 2 (12.2125)(28.2125) cos DAC
cos DAC = (12.2125² + 28.2125² - 16²)/(2 (12.2125)(28.2125) ) = 1
That's a surprise, DAC maxes out at a right angle
90 = 2x - 12
102 = 2x
x = 51
Answer: 6 < x < 51
