1. **State the problem:** Solve the equation $6x + 9 = 2x - 5$ for $x$. 2. **Write down the equation:** $$6x + 9 = 2x - 5$$ 3. **Isolate the variable terms on one side:** Subtract $2x$ from both sides: $$6x + 9 - \cancel{2x} = \cancel{2x} - 5 - 2x$$ which simplifies to $$6x - 2x + 9 = -5$$ 4. **Simplify the left side:** $$4x + 9 = -5$$ 5. **Isolate the term with $x$ by subtracting 9 from both sides:** $$4x + 9 - \cancel{9} = -5 - 9$$ which simplifies to $$4x = -14$$ 6. **Solve for $x$ by dividing both sides by 4:** $$\frac{4x}{\cancel{4}} = \frac{-14}{\cancel{4}}$$ which simplifies to $$x = -\frac{14}{4}$$ 7. **Simplify the fraction:** $$x = -\frac{7}{2}$$ **Final answer:** $$x = -\frac{7}{2}$$