1. **State the problem:** Evaluate the expression $4 \cdot 61 - 3x$ when $x = \frac{1}{3}$. 2. **Substitute the value of $x$:** Replace $x$ with $\frac{1}{3}$ in the expression: $$4 \cdot 61 - 3 \times \frac{1}{3}$$ 3. **Calculate $4 \cdot 61$:** $$4 \cdot 61 = 244$$ 4. **Calculate $3 \times \frac{1}{3}$:** $$3 \times \frac{1}{3} = \cancel{3} \times \frac{1}{\cancel{3}} = 1$$ 5. **Substitute back and simplify:** $$244 - 1 = 243$$ 6. **Check answers given:** The answers listed (32, -32, 61, -61) do not match the evaluated result 243, so none of those are correct for this expression. --- Next, evaluate the following expressions with $x = \frac{1}{3}$: 7. $5 \times 2x = 5 \times 2 \times \frac{1}{3} = 5 \times \frac{2}{3} = \frac{10}{3} \approx 3.33$ 8. $6 \times -2x = 6 \times -2 \times \frac{1}{3} = 6 \times -\frac{2}{3} = -4$ 9. $7 \times (-2)(-x) = 7 \times (-2) \times -\frac{1}{3} = 7 \times \frac{2}{3} = \frac{14}{3} \approx 4.67$ 10. $8 \times 2x = 8 \times 2 \times \frac{1}{3} = 8 \times \frac{2}{3} = \frac{16}{3} \approx 5.33$ 11. $9 \times -2x = 9 \times -2 \times \frac{1}{3} = 9 \times -\frac{2}{3} = -6$ **Final answers:** - $4 \cdot 61 - 3x = 243$ - $5 \times 2x = \frac{10}{3}$ - $6 \times -2x = -4$ - $7 \times (-2)(-x) = \frac{14}{3}$ - $8 \times 2x = \frac{16}{3}$ - $9 \times -2x = -6$