1. **State the problem:** Solve the equation $5(K+4) = 2(2.5K - 3) + 12$ for $K$. 2. **Write the formula and rules:** Use the distributive property to expand both sides and then isolate $K$. 3. **Expand both sides:** $$5(K+4) = 5K + 20$$ $$2(2.5K - 3) = 5K - 6$$ So the equation becomes: $$5K + 20 = 5K - 6 + 12$$ 4. **Simplify the right side:** $$5K + 20 = 5K + 6$$ 5. **Subtract $5K$ from both sides:** $$\cancel{5K} + 20 = \cancel{5K} + 6$$ $$20 = 6$$ 6. **Analyze the result:** The statement $20 = 6$ is false, which means there is no solution for $K$. **Final answer:** There is no solution to the equation; it is inconsistent.