Question
16. Find the Error A student is writing an inequality for the expression a minimum donation of \( \$ 25 \). Find the student's mistake and correct it. \( d \leq 25 \)
Ask by Fuentes Love. in the United States
Jan 20,2025
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Answer
The student's mistake was using \( d \leq 25 \) to represent a minimum donation of \$25. The correct inequality should be \( d \geq 25 \) to ensure the donation is at least \$25.
Solution
The student is tasked with writing an inequality that represents **a minimum donation of \$25**. This means that the donation should be **at least** \$25.
### **Student's Mistake:**
The student wrote the inequality as:
\[ d \leq 25 \]
This inequality suggests that the donation \( d \) is **less than or equal to** \$25, which implies that the donation could be \$25 or **less**, contradicting the idea of a **minimum** donation.
### **Correction:**
To correctly represent a **minimum** donation, the inequality should state that \( d \) is **greater than or equal to** \$25. Therefore, the correct inequality is:
\[ d \geq 25 \]
### **Explanation:**
- **\( d \geq 25 \)** means the donation \( d \) is **at least** \$25.
- This ensures that the donation meets or exceeds the minimum required amount.
**Correct Inequality:**
\[ d \geq 25 \]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
The student's mistake lies in using the "less than or equal to" symbol (≤) for a minimum donation. Since the expression indicates that the minimum donation is \( \$ 25 \), the correct inequality should reflect that donations must be at least \( \$ 25 \). Therefore, the corrected inequality is: \( d \geq 25 \). When writing inequalities, it's important to pay attention to the context—"minimum" should signal that the quantity can only be equal to or above a certain threshold. Remember, inequalities are all about expressing relationships clearly, so it helps to think about what the problem is saying!
