14. Which two expressions are equivalent? A. \( 7(3+x) \) and \( 7 \cdot 3+3 \cdot x \) B. \( 7+3+x \) and \( (7+3)+x \) C. \( 7 \cdot x \cdot 3 \) and \( 7(x+3) \) D. \( 7 \div(3-x) \) and \( 7 \div(x-3) \)

Let's evaluate each pair of expressions to determine which ones are equivalent: **A. \( 7(3+x) \) and \( 7 \cdot 3 + 3 \cdot x \)** - **First Expression:** \( 7(3 + x) = 21 + 7x \) - **Second Expression:** \( 7 \cdot 3 + 3 \cdot x = 21 + 3x \) - **Conclusion:** These expressions are **not equivalent** because \( 7x \neq 3x \). --- **B. \( 7 + 3 + x \) and \( (7 + 3) + x \)** - **First Expression:** \( 7 + 3 + x = 10 + x \) - **Second Expression:** \( (7 + 3) + x = 10 + x \) - **Conclusion:** These expressions are **equivalent**. --- **C. \( 7 \cdot x \cdot 3 \) and \( 7(x + 3) \)** - **First Expression:** \( 7 \cdot x \cdot 3 = 21x \) - **Second Expression:** \( 7(x + 3) = 7x + 21 \) - **Conclusion:** These expressions are **not equivalent** because \( 21x \neq 7x + 21 \). --- **D. \( 7 \div (3 - x) \) and \( 7 \div (x - 3) \)** - **First Expression:** \( \frac{7}{3 - x} \) - **Second Expression:** \( \frac{7}{x - 3} \) - **Conclusion:** These expressions are **not equivalent** because \( \frac{7}{3 - x} = -\frac{7}{x - 3} \). --- **Final Answer:** **Option B** contains two equivalent expressions. **Answer:** **Option B** contains two equivalent expressions.