1. **State the problem:** Solve the equation $6(x + 2) - 3x = -3(x - 21) + 7$ for $x$. 2. **Write down the equation:** $$6(x + 2) - 3x = -3(x - 21) + 7$$ 3. **Apply the distributive property:** $$6x + 12 - 3x = -3x + 63 + 7$$ 4. **Simplify both sides:** $$3x + 12 = -3x + 70$$ 5. **Add $3x$ to both sides to collect $x$ terms on the left:** $$3x + 3x + 12 = 70$$ $$6x + 12 = 70$$ 6. **Subtract 12 from both sides:** $$6x = 70 - 12$$ $$6x = 58$$ 7. **Divide both sides by 6 to solve for $x$:** $$x = \frac{58}{6} = \frac{29}{3}$$ **Final answer:** $$x = \frac{29}{3}$$