Question
Fill in each box with either < or > \( \begin{array}{l}\text { (A) } 3 \square-8 \\ \text { (B) }-9 \square-2 \\ \text { (C) }-4 \square-7\end{array} \)
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Jan 07,2025
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Tutor-Verified Answer
Answer
\[
\begin{array}{l}
\text{(A)}\ 3 > -8 \\
\text{(B)}\ -9 < -2 \\
\text{(C)}\ -4 > -7
\end{array}
\]
Solution
Sure, let's compare each pair of numbers and determine whether to use `<` or `>`.
**(A) \(3 \square -8\)**
- **Comparison:** \(3\) vs. \(-8\)
- **Since \(3\) is greater than \(-8\),** the correct symbol is `>`.
- **Result:** \(3 > -8\)
**(B) \(-9 \square -2\)**
- **Comparison:** \(-9\) vs. \(-2\)
- **Since \(-9\) is less than \(-2\),** the correct symbol is `<`.
- **Result:** \(-9 < -2\)
**(C) \(-4 \square -7\)**
- **Comparison:** \(-4\) vs. \(-7\)
- **Since \(-4\) is greater than \(-7\),** the correct symbol is `>`.
- **Result:** \(-4 > -7\)
**Final Filled Expressions:**
\[
\begin{array}{l}
\text{(A)}\ 3 > -8 \\
\text{(B)}\ -9 < -2 \\
\text{(C)}\ -4 > -7
\end{array}
\]
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Simplify this solution Extra Insights
To solve the inequalities: 1. For (A) \(3 \square - 8\), - If we let \(x = 3\) and \(x = -8\), \(3 > -8\), so we use \(>\). 2. For (B) \(-9 \square -2\), - Here, \(-9 < -2\) so we use \(<\). 3. For (C) \(-4 \square -7\), - Similarly, \(-4 > -7\), so we use \(>\). Putting it all together, it looks like this: (A) \(3 > -8\) (B) \(-9 < -2\) (C) \(-4 > -7\) Thus the completed boxes are: \(>\), \(<\), \(>\).
