Answer:
x = 6
Step-by-step explanation:
Line segment AB is the midsegment of triangle XYZ as it connects the midpoints of sides XY and YZ.
According to the Triangle Midsegment Theorem, the line segment connecting the midpoints of two sides of a triangle is equal to half the length of that third side. Therefore:
[tex]\overline{AB}=\dfrac{1}{2}\;\overline{XZ}[/tex]
Substitute the expressions for each line segment into the equation, and solve for x:
[tex]3x-1=\dfrac{1}{2}(34)\\\\\\3x-1=17\\\\\\3x-1+1=17+1\\\\\\3x=18\\\\\\\dfrac{3x}{3}=\dfrac{18}{3}\\\\\\x=6[/tex]
Therefore, the value of x is:
[tex]\LARGE\boxed{\boxed{x=6}}[/tex]
