1. **State the problem:** We are given a trapezoid with segments labeled with expressions involving $x$. We need to find the length of segment $EF$. 2. **Analyze the given information:** - Segment $AD = x - 5$ - Segment $BC = 2x - 6$ - Segment $EF = x$ - The red tick marks indicate equal lengths: $EF$ has two red ticks, matching $BC$ which also has two red ticks, so $EF = BC$. 3. **Set up the equation:** Since $EF$ and $BC$ are equal, $$x = 2x - 6$$ 4. **Solve for $x$:** $$x = 2x - 6$$ Subtract $2x$ from both sides: $$\cancel{x} - 2x = \cancel{2x} - 2x - 6$$ $$-x = -6$$ Multiply both sides by $-1$: $$x = 6$$ 5. **Find the length of $EF$:** Since $EF = x$, then $$EF = 6$$ 6. **Check the other segments:** - $AD = x - 5 = 6 - 5 = 1$ - $BC = 2x - 6 = 2(6) - 6 = 12 - 6 = 6$ The lengths are consistent with the tick marks. **Final answer:** $$EF = 6$$