1. **State the problem:** Solve for $x$ in the equation $5x - 7 = 17 - 3(2 - x)$. 2. **Write down the equation:** $$5x - 7 = 17 - 3(2 - x)$$ 3. **Distribute the $-3$ on the right side:** $$5x - 7 = 17 - 6 + 3x$$ 4. **Simplify the right side:** $$5x - 7 = 11 + 3x$$ 5. **Bring all $x$ terms to one side and constants to the other:** Subtract $3x$ from both sides: $$5x - 3x - 7 = 11$$ Simplify: $$2x - 7 = 11$$ 6. **Add 7 to both sides:** $$2x = 18$$ 7. **Divide both sides by 2 to isolate $x$:** $$x = \frac{18}{2} = 9$$ **Final answer:** $$x = 9$$