1. **State the problem:** We are given that line segment \(\overline{AB}\) is congruent to line segment \(\overline{CD}\), meaning their lengths are equal. We need to find the value of \(x\). 2. **Write the equation:** Since \(\overline{AB} \cong \overline{CD}\), their lengths are equal: $$2x + 11 = 4x + 5$$ 3. **Solve for \(x\):** - Subtract \(2x\) from both sides: $$11 = 2x + 5$$ - Subtract 5 from both sides: $$11 - 5 = 2x$$ $$6 = 2x$$ - Divide both sides by 2: $$x = \frac{6}{2} = 3$$ 4. **Conclusion:** The value of \(x\) is \(3\).