1. **State the problem:** Solve the equation $2x - 7 [ x - (3x + 2)] = 9$ for $x$. 2. **Apply the distributive property inside the brackets:** Inside the brackets, simplify $x - (3x + 2)$. 3. **Simplify inside the brackets:** $$x - (3x + 2) = x - 3x - 2 = -2x - 2$$ 4. **Substitute back into the equation:** $$2x - 7(-2x - 2) = 9$$ 5. **Distribute $-7$ over $-2x - 2$:** $$2x + 14x + 14 = 9$$ 6. **Combine like terms:** $$16x + 14 = 9$$ 7. **Isolate the variable term by subtracting 14 from both sides:** $$16x + \cancel{14} - \cancel{14} = 9 - 14$$ $$16x = -5$$ 8. **Solve for $x$ by dividing both sides by 16:** $$x = \frac{-5}{16}$$ **Final answer:** $$x = -\frac{5}{16}$$