Question
29 An inequality is shown.
\[ \frac{1}{8}
Ask by Hodges O'Quinn. in the United States
Jan 24,2025
Ask by Hodges O'Quinn. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \frac{1}{5} \) does not satisfy the inequality \( \frac{1}{8} < x < 18\% \).
Solution
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 %.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
Let’s break it down! First, to clarify the inequality, \( 18\% \) is equal to \( 0.18 \) as a decimal. Therefore, we need to find values of \( x \) that are greater than \( 0.125 \) (which is \( \frac{1}{8} \)) and less than \( 0.18 \). Now, looking at the answer choice, \( \frac{1}{5} \) equals \( 0.20 \), which does not satisfy the inequality since \( 0.20 \) is greater than \( 0.18 \). So, it's a no-go for \( \frac{1}{5} \)! Keep searching for a value between \( \frac{1}{8} \) and \( 0.18 \) to find a true solution!
