1. **State the problem:** Solve the inequality $2k - 7 < 7k + 6$ for $k$. 2. **Write the inequality:** $$2k - 7 < 7k + 6$$ 3. **Isolate the variable terms on one side:** Subtract $2k$ from both sides: $$\cancel{2k} - 7 < 7k + 6 - \cancel{2k}$$ which simplifies to $$-7 < 5k + 6$$ 4. **Isolate the constant terms on the other side:** Subtract 6 from both sides: $$-7 - 6 < 5k + \cancel{6} - \cancel{6}$$ which simplifies to $$-13 < 5k$$ 5. **Solve for $k$ by dividing both sides by 5:** Since 5 is positive, the inequality direction stays the same: $$\frac{-13}{\cancel{5}} < \frac{5k}{\cancel{5}}$$ which simplifies to $$-\frac{13}{5} < k$$ 6. **Rewrite the solution:** $$k > -\frac{13}{5}$$ **Answer:** The solution to the inequality is $k > -\frac{13}{5}$.