1. **State the problem:** Solve the equation $5 \cdot x + 10 \cdot (30 - x) = 230$ for $x$. 2. **Write the equation:** $$5x + 10(30 - x) = 230$$ 3. **Distribute the 10:** $$5x + 10 \times 30 - 10x = 230$$ $$5x + 300 - 10x = 230$$ 4. **Combine like terms:** $$5x - 10x + 300 = 230$$ $$-5x + 300 = 230$$ 5. **Isolate the term with $x$ by subtracting 300 from both sides:** $$-5x + \cancel{300} - \cancel{300} = 230 - 300$$ $$-5x = -70$$ 6. **Divide both sides by $-5$ to solve for $x$:** $$\frac{-5x}{\cancel{-5}} = \frac{-70}{\cancel{-5}}$$ $$x = 14$$ **Final answer:** $$x = 14$$