1. **State the problem:** Solve the equation $9x + 16 = 4x - 19$ for $x$. 2. **Write down the formula and rules:** To solve linear equations, we isolate the variable on one side by performing inverse operations. 3. **Step-by-step solution:** - Subtract $4x$ from both sides: $$9x + 16 - 4x = 4x - 19 - 4x$$ - Simplify: $$5x + 16 = -19$$ - Subtract $16$ from both sides: $$5x + 16 - 16 = -19 - 16$$ - Simplify: $$5x = -35$$ - Divide both sides by $5$: $$\frac{\cancel{5}x}{\cancel{5}} = \frac{-35}{5}$$ - Simplify: $$x = -7$$ 4. **Final answer:** $$x = -7$$