1. **State the problem:** Priya has 5 pencils, each of length $x$ inches. When lined up end to end, their total length is 34.5 inches. 2. **Formulate the equation:** Since there are 5 pencils each of length $x$, the total length is $5 \times x$. 3. **Write the equation:** $$5x = 34.5$$ 4. **Check the options:** - A. $5 + x = 34.5$ (Incorrect, addition is not the right operation here) - B. $5x = 34.5$ (Correct, multiplication represents total length) - C. $34.5 \div 5 = x$ (Correct, dividing total length by number of pencils gives length of one) - D. $34.5 - 5 = x$ (Incorrect, subtraction is not appropriate) - E. $x = (34.5) \cdot 5$ (Incorrect, this would give a length 5 times too large) 5. **Solve for $x$:** $$x = \frac{34.5}{5}$$ 6. **Simplify:** $$x = \cancel{\frac{34.5}{\cancel{5}}} = 6.9$$ 7. **Interpretation:** Each pencil is 6.9 inches long. **Final answer:** $$x = 6.9$$