1. **State the problem:** Solve for $d$ in the equation $$6d - \frac{11}{2} = 2d - \frac{13}{2}$$. 2. **Isolate the variable terms on one side:** Subtract $2d$ from both sides to get all $d$ terms on the left. $$6d - 2d - \frac{11}{2} = 2d - 2d - \frac{13}{2}$$ 3. **Simplify the equation:** $$4d - \frac{11}{2} = - \frac{13}{2}$$ 4. **Isolate the $d$ term:** Add $\frac{11}{2}$ to both sides. $$4d - \frac{11}{2} + \frac{11}{2} = - \frac{13}{2} + \frac{11}{2}$$ $$4d = - \frac{13}{2} + \frac{11}{2}$$ 5. **Combine the fractions on the right:** $$4d = - \frac{13 - 11}{2} = - \frac{2}{2} = -1$$ 6. **Solve for $d$ by dividing both sides by 4:** $$d = \frac{-1}{4}$$ 7. **Show cancellation step:** $$d = \frac{\cancel{ -1}}{\cancel{4}} = -\frac{1}{4}$$ **Final answer:** $$d = -\frac{1}{4}$$