1. **State the problem:** Solve the linear equation $$22 - 8x = 2x + 9$$ for $x$. 2. **Write down the formula and rules:** To solve for $x$, we want to isolate $x$ on one side of the equation. We do this by moving all terms involving $x$ to one side and constants to the other. 3. **Move terms involving $x$ to one side:** Add $8x$ to both sides: $$22 - \cancel{8x} + 8x = 2x + 8x + 9$$ which simplifies to $$22 = 10x + 9$$ 4. **Move constants to the other side:** Subtract $9$ from both sides: $$22 - 9 = 10x + \cancel{9} - 9$$ which simplifies to $$13 = 10x$$ 5. **Isolate $x$ by dividing both sides by 10:** $$\frac{13}{\cancel{10}} = x \cdot \frac{\cancel{10}}{10}$$ which simplifies to $$x = \frac{13}{10}$$ 6. **Final answer:** $$x = \frac{13}{10}$$ or $1.3$. This means the solution to the equation is $x = 1.3$.