29 An inequality is shown. \[ \frac{1}{8}

Ask by Hodges O'Quinn. in the United States

Jan 24,2025

To determine whether \( x = \frac{1}{5} \) satisfies the inequality: \[ \frac{1}{8} < x < 18\% \] Let's analyze each part of the inequality step by step. 1. **Convert All Values to Decimal Form:** - \( \frac{1}{8} = 0.125 \) - \( 18\% = 0.18 \) - \( \frac{1}{5} = 0.2 \) 2. **Compare \( x \) to the Inequality Bounds:** - Lower bound: \( 0.125 < x \) - Upper bound: \( x < 0.18 \) 3. **Check if \( x = 0.2 \) Satisfies the Inequality:** - **Lower Bound Check:** \( 0.125 < 0.2 \) → **True** - **Upper Bound Check:** \( 0.2 < 0.18 \) → **False** Since \( x = 0.2 \) does not satisfy the upper bound of the inequality, it **does not** make the entire inequality true. **Conclusion:** Option **A (\( \frac{1}{5} \))** does **not** satisfy the inequality \( \frac{1}{8} < x < 18\% \). **Answer:** No, \( \frac{1}{5} \) does not satisfy the inequality because it is greater than 18 %.