1. **State the problem:** Solve the equation $7(2k+1) = 3(4k-2)$ for $k$. 2. **Apply the distributive property:** Multiply out both sides: $$7 \times 2k + 7 \times 1 = 3 \times 4k - 3 \times 2$$ which simplifies to $$14k + 7 = 12k - 6$$ 3. **Isolate variable terms:** Subtract $12k$ from both sides: $$14k + 7 - \cancel{12k} = 12k - 6 - \cancel{12k}$$ which simplifies to $$2k + 7 = -6$$ 4. **Isolate the constant term:** Subtract 7 from both sides: $$2k + 7 - \cancel{7} = -6 - \cancel{7}$$ which simplifies to $$2k = -13$$ 5. **Solve for $k$:** Divide both sides by 2: $$\frac{2k}{\cancel{2}} = \frac{-13}{\cancel{2}}$$ which simplifies to $$k = -\frac{13}{2}$$ **Final answer:** $$k = -\frac{13}{2}$$