1. **State the problem:** Solve the equation $6 - 5k = 14 + 3k$ and find the value of $k$. 2. **Write the equation:** $$6 - 5k = 14 + 3k$$ 3. **Isolate the variable terms on one side:** Subtract $14$ from both sides and add $5k$ to both sides: $$6 - 5k - 14 = 14 + 3k - 14$$ $$6 - 14 - 5k = 3k$$ $$-8 - 5k = 3k$$ Add $5k$ to both sides: $$-8 - 5k + 5k = 3k + 5k$$ $$-8 = 8k$$ 4. **Solve for $k$ by dividing both sides by 8:** $$\frac{-8}{\cancel{8}} = \frac{8k}{\cancel{8}}$$ $$-1 = k$$ 5. **Conclusion:** The solution to the equation is $k = -1$. **Note:** The answer is not 4; it is $-1$ based on the correct algebraic steps.