1. **State the problem:** We are given the equation $8d + 1 = -8$ and asked to analyze the related equation $10c - 3 = 8$. 2. **Solve for $d$ in the first equation:** $$8d + 1 = -8$$ Subtract 1 from both sides: $$8d + \cancel{1} - \cancel{1} = -8 - 1$$ $$8d = -9$$ Divide both sides by 8: $$\frac{8d}{\cancel{8}} = \frac{-9}{8}$$ $$d = -\frac{9}{8}$$ 3. **Analyze the second equation $10c - 3 = 8$:** Add 3 to both sides: $$10c - \cancel{3} + \cancel{3} = 8 + 3$$ $$10c = 11$$ Divide both sides by 10: $$\frac{10c}{\cancel{10}} = \frac{11}{10}$$ $$c = \frac{11}{10}$$ 4. **Summary:** - From $8d + 1 = -8$, we find $d = -\frac{9}{8}$. - From $10c - 3 = 8$, we find $c = \frac{11}{10}$. These are the solutions for $d$ and $c$ based on the given equations.