1. **State the problem:** Solve the equation $5(2x+1)=4(3x-7)$ for $x$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside. $$5 \times 2x + 5 \times 1 = 4 \times 3x - 4 \times 7$$ which simplifies to $$10x + 5 = 12x - 28$$ 3. **Isolate variable terms on one side:** Subtract $10x$ from both sides. $$\cancel{10x} + 5 = 12x - 28 - \cancel{10x}$$ which simplifies to $$5 = 2x - 28$$ 4. **Isolate the constant term:** Add $28$ to both sides. $$5 + 28 = 2x - 28 + 28$$ which simplifies to $$33 = 2x$$ 5. **Solve for $x$:** Divide both sides by $2$. $$\frac{33}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ which simplifies to $$x = \frac{33}{2}$$ **Final answer:** $$x = \frac{33}{2}$$