29 An inequality is shown. Which value of \( x \) makes the inequality true? A \( \frac{1}{5}

Ask by Campbell Salazar. in the United States

Jan 24,2025

To determine which value of \( x \) makes the inequality \( \frac{1}{5} < x < 18\% \) true, we first need to convert all values into a comparable format. 1. **Convert \( \frac{1}{5} \) to decimal:** \[ \frac{1}{5} = 0.2 \] 2. **Convert \( 18\% \) to decimal:** \[ 18\% = \frac{18}{100} = 0.18 \] Now, the inequality can be rewritten as: \[ 0.2 < x < 0.18 \] Next, we will evaluate each option to see if it satisfies the inequality. - **Option A:** \( \frac{1}{5} < x < 18\% \) is the inequality itself, not a value. - **Option B:** \( x = 1.6 \) - Check: \( 0.2 < 1.6 < 0.18 \) (False) - **Option C:** \( x = 0.09 \) - Check: \( 0.2 < 0.09 < 0.18 \) (False) - **Option D:** \( x = \sqrt{0.02} \) - Calculate \( \sqrt{0.02} \): \[ \sqrt{0.02} \approx 0.1414 \] - Check: \( 0.2 < 0.1414 < 0.18 \) (False) None of the options satisfy the inequality \( 0.2 < x < 0.18 \). It seems there might be a misunderstanding in the inequality's bounds. The correct interpretation should be \( 0.18 < x < 0.2 \). Let's check the values again: - **Option B:** \( 1.6 \) is not in the range. - **Option C:** \( 0.09 \) is not in the range. - **Option D:** \( \sqrt{0.02} \approx 0.1414 \) is also not in the range. Since none of the provided options satisfy the inequality, it appears there may be an error in the options given. Please verify the inequality or the options provided.