Answer:
x = 5
Step-by-step explanation:
To do this, you need to use the Thales theorem.
You can actually apply this theorem and choose two sides of the figure to do it.
In this case, I will choose segment LM and MN and look for a ratio with DE and EF like this:
LM/MN = DE/EF
This theorem states that you can stablish a ratio between two segments assuming that you have at least two paralels lines, like DL || EM || FN
Therefore, it's time to replace the values of those segments and solve for X:
LM/MN = DE/EF
14/16 = 6x -9 / 4x + 4
7/8 = 6x - 9 / 4x + 4
7(4x+4) = 8(6x-9)
28x + 28 = 48x - 72
72 + 28 = 48x - 28x
100 = 20x
x = 100/20
x = 5
