1. **State the problem:** Find the perimeter of the trapezoid with sides labeled as $9x$, $5x + 1$, $8x - 2$, and $17x - 6$. 2. **Recall the formula for perimeter:** The perimeter $P$ of a polygon is the sum of the lengths of all its sides. 3. **Write the expression for the perimeter:** $$P = 9x + (5x + 1) + (8x - 2) + (17x - 6)$$ 4. **Combine like terms:** $$P = 9x + 5x + 1 + 8x - 2 + 17x - 6$$ 5. **Group the $x$ terms and constants:** $$P = (9x + 5x + 8x + 17x) + (1 - 2 - 6)$$ 6. **Add the coefficients of $x$:** $$9x + 5x + 8x + 17x = (9 + 5 + 8 + 17)x = 39x$$ 7. **Add the constants:** $$1 - 2 - 6 = -7$$ 8. **Write the simplified perimeter:** $$P = 39x - 7$$ **Final answer:** The perimeter of the trapezoid is $$\boxed{39x - 7}$$.