1. **State the problem:** Priyaha has 5 pencils, each of length $x$ inches. When lined up end to end, their total length is 34.5 inches. 2. **Understand the situation:** The total length of 5 pencils each $x$ inches long is $5 \times x$. 3. **Form the equation:** Since the total length is 34.5 inches, the equation is: $$5x = 34.5$$ 4. **Check each option:** - A. $5 + x = 34.5$ means adding 5 inches to $x$, which is incorrect. - B. $5x = 34.5$ correctly represents 5 pencils each $x$ inches long totaling 34.5 inches. - C. $34.5 \div 5 = x$ is the same as $x = \frac{34.5}{5}$, which correctly solves for $x$. - D. $34.5 - 5 = x$ subtracts 5 inches from total length, which is incorrect. - E. $x = \frac{34.5}{5}$ correctly expresses $x$ as the total length divided by 5. 5. **Final answer:** The correct equations are B, C, and E.