For problems 22 through 24, find the value of x.

Answer:
see explanation
Step-by-step explanation:
The segment bisecting 2 sides of the triangles are midsegments and are all one half the measure of the third side.
22
x - 4 = 0.5 × 17 = 8.5 ( add 4 to both sides )
x = 12.5
23
x + 2 = 0.5 × 38 = 19 ( subtract 2 from both sides )
x = 17
24
5x - 4 = 2 × 8 = 16 ( add 4 to both sides )
5x = 20 ( divide both sides by 5 )
x = 4
All of your shapes are formed like this: pick a triangle, and connect the middle points of two sides. In all those cases, you have that the inner triangle is similar to the whole triangle, with scale factor 1/2.
Look at the attached picture. ABC is similar to CDE, and since the correspondent sides are one the double of the other (AC=2DC and BC=2CE), we deduce that AB=2DE.
So, in your exercises, you'll always have to setup this equation: the inner segment is half of the base. For example, in the first exercise, you have
[tex]x-4=\dfrac{17}{2} \iff 2x-8=17 \iff 2x=25 \iff x=12.5[/tex]
Work similarly for the second and third triangle and you'll be done