1. **State the problem:** Solve the equation $5(x + 3) = 4(2x - 14) - 1$ for $x$. 2. **Write down the equation:** $$5(x + 3) = 4(2x - 14) - 1$$ 3. **Apply the distributive property:** $$5 \times x + 5 \times 3 = 4 \times 2x - 4 \times 14 - 1$$ $$5x + 15 = 8x - 56 - 1$$ 4. **Simplify the right side:** $$5x + 15 = 8x - 57$$ 5. **Bring all terms involving $x$ to one side and constants to the other:** $$5x + 15 = 8x - 57$$ Subtract $5x$ from both sides: $$\cancel{5x} + 15 = 8x - 57 - \cancel{5x}$$ $$15 = 3x - 57$$ 6. **Add 57 to both sides to isolate the term with $x$:** $$15 + 57 = 3x - 57 + 57$$ $$72 = 3x$$ 7. **Divide both sides by 3 to solve for $x$:** $$\frac{72}{\cancel{3}} = \frac{3x}{\cancel{3}}$$ $$24 = x$$ **Final answer:** $$x = 24$$