1. **State the problem:** We are given a triangle XYZ with segment AB as the midsegment. AB is labeled as $3x - 1$ and side XZ is labeled as 34. We need to find the value of $x$. 2. **Recall the midsegment theorem:** The midsegment of a triangle is parallel to the third side and its length is half the length of that side. 3. **Set up the equation:** Since AB is the midsegment parallel to XZ, we have: $$AB = \frac{1}{2} XZ$$ Substitute the given lengths: $$3x - 1 = \frac{1}{2} \times 34$$ 4. **Simplify the right side:** $$3x - 1 = 17$$ 5. **Solve for $x$:** Add 1 to both sides: $$3x - \cancel{1} + 1 = 17 + 1$$ $$3x = 18$$ Divide both sides by 3: $$\frac{\cancel{3}x}{\cancel{3}} = \frac{18}{3}$$ $$x = 6$$ **Final answer:** $$x = 6$$