1. **State the problem:** Solve the equation $$\frac{x + 51}{7} + 24 = 35$$ for $x$. 2. **Isolate the fraction:** Subtract 24 from both sides to get $$\frac{x + 51}{7} = 35 - 24$$ 3. **Simplify the right side:** $$35 - 24 = 11$$ so the equation becomes $$\frac{x + 51}{7} = 11$$ 4. **Eliminate the denominator:** Multiply both sides by 7: $$7 \times \frac{x + 51}{7} = 7 \times 11$$ 5. **Cancel the 7 in the denominator:** $$\cancel{7} \times \frac{x + 51}{\cancel{7}} = 77$$ which simplifies to $$x + 51 = 77$$ 6. **Solve for $x$:** Subtract 51 from both sides: $$x + 51 - 51 = 77 - 51$$ $$x = 26$$ **Final answer:** $$x = 26$$