1. **State the problem:** Solve the equation $$35=\frac{1}{2}\cdot (x+30)$$ for $x$. 2. **Use the formula and rules:** To solve for $x$, we need to isolate $x$ on one side. Since $x$ is inside parentheses multiplied by $\frac{1}{2}$, we first undo the multiplication by multiplying both sides by 2. 3. **Multiply both sides by 2:** $$2 \times 35 = 2 \times \frac{1}{2} \cdot (x+30)$$ $$70 = \cancel{2} \times \frac{1}{\cancel{2}} \cdot (x+30)$$ $$70 = x + 30$$ 4. **Subtract 30 from both sides to isolate $x$:** $$70 - 30 = x + 30 - 30$$ $$40 = x$$ 5. **Final answer:** $$x = 40$$ This means the value of $x$ that satisfies the equation is 40.