1. **State the problem:** Solve the equation $$31 = 3u - 14$$ for the variable $$u$$. 2. **Write the formula and rules:** To solve for $$u$$, we need to isolate $$u$$ on one side of the equation. This involves two steps: first, add 14 to both sides to cancel the $$-14$$, then divide both sides by 3 to solve for $$u$$. 3. **Step 1: Add 14 to both sides** $$31 + 14 = 3u - 14 + 14$$ $$45 = 3u$$ 4. **Step 2: Divide both sides by 3** $$\frac{45}{3} = \frac{3u}{3}$$ Show cancellation: $$\frac{\cancel{45}}{\cancel{3}} = \frac{\cancel{3}u}{\cancel{3}}$$ $$15 = u$$ 5. **Final answer:** $$u = 15$$ This means the value of $$u$$ that satisfies the equation is 15.