1. **State the problem:** Solve the equation $9(x+7)=4(x-3)$ for $x$. 2. **Write the formula and rules:** We use the distributive property to expand both sides and then isolate $x$ by combining like terms. 3. **Expand both sides:** $$9(x+7) = 9x + 63$$ $$4(x-3) = 4x - 12$$ So the equation becomes: $$9x + 63 = 4x - 12$$ 4. **Isolate $x$ terms on one side:** Subtract $4x$ from both sides: $$9x + 63 - \cancel{4x} = 4x - 12 - \cancel{4x}$$ $$5x + 63 = -12$$ 5. **Isolate the constant term:** Subtract 63 from both sides: $$5x + 63 - \cancel{63} = -12 - \cancel{63}$$ $$5x = -75$$ 6. **Solve for $x$ by dividing both sides by 5:** $$x = \frac{-75}{5}$$ $$x = -15$$ **Final answer:** $$x = -15$$