1. **State the problem:** We have a square ABCD with sides AB and BC given as algebraic expressions: AB = $x + 6$ and BC = $2x - 1$. We need to find the length of side DC. 2. **Recall properties of a square:** All sides of a square are equal in length. Therefore, AB = BC = CD = DA. 3. **Set up the equation:** Since AB = BC, we have: $$x + 6 = 2x - 1$$ 4. **Solve for $x$:** Subtract $x$ from both sides: $$6 = x - 1$$ Add 1 to both sides: $$6 + 1 = x$$ $$x = 7$$ 5. **Find the length of DC:** Since DC = AB, substitute $x = 7$ into $x + 6$: $$DC = 7 + 6 = 13$$ 6. **Answer:** The length of line segment DC is 13 units. **Final answer:** 13 units