1. **State the problem:** Solve the equation $$5w + 8 = 83$$ for the variable $$w$$. 2. **Write the formula and rules:** To solve for $$w$$, we need to isolate $$w$$ on one side of the equation. This involves undoing addition and multiplication by performing inverse operations. 3. **Step 1: Subtract 8 from both sides** to undo the addition of 8: $$5w + 8 - 8 = 83 - 8$$ which simplifies to $$5w = 75$$ 4. **Step 2: Divide both sides by 5** to undo the multiplication by 5: $$\frac{5w}{\cancel{5}} = \frac{75}{\cancel{5}}$$ which simplifies to $$w = 15$$ 5. **Final answer:** $$w = 15$$ This means the value of $$w$$ that satisfies the equation is 15.