The length of CB is x + 7 .
To find CB, we can use the midsegment theorem.
The midsegment theorem states that the midsegment of a trapezoid is parallel to both bases and its length is equal to the average of the lengths of the bases.
In the diagram, MJ is the midsegment of trapezoid CBAD. Therefore, MJ is parallel to CB and AD, and MJ = (CB + AD) / 2.
We are given that MJ = 4x - 23. We are also given that AD = 12. Therefore, we can set up the following equation:
4x - 23 = (CB + 12) / 2
Multiplying both sides by 2, we get:
8x - 46 = CB + 12
Subtracting 12 from both sides, we get:
8x - 58 = CB
Adding 58 to both sides, we get:
8x = CB + 58
Dividing both sides by 8, we get:
CB= x + 7
Therefore, the length of CB is x + 7.