1. **State the problem:** Translate the sentence "Twice the difference of a number and 3 is 5" into an equation using the variable $w$ for the unknown number. 2. **Understand the key phrases:** - "Difference of a number and 3" means $w - 3$. - "Twice" means multiply by 2. - "Is 5" means equals 5. 3. **Write the equation:** $$2 \times (w - 3) = 5$$ 4. **Simplify and solve the equation:** $$2(w - 3) = 5$$ $$2w - 6 = 5$$ 5. **Isolate $w$ by adding 6 to both sides:** $$2w - 6 + 6 = 5 + 6$$ $$2w = 11$$ 6. **Divide both sides by 2 to solve for $w$:** $$\cancel{2}w = \frac{11}{\cancel{2}}$$ $$w = \frac{11}{2}$$ **Final answer:** $$w = \frac{11}{2}$$