Let's solve the expression step-by-step first.
The original expression is:
\[ -6 + 3 \cdot 5 , _ , \sqrt{16} + 32 \div 6 \]
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Calculate \(\sqrt{16}\): \[ \sqrt{16} = 4 \]
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Rewrite the expression: \[ -6 + 3 \cdot 5 , _ , 4 + 32 \div 6 \]
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Calculate \(3 \cdot 5\) and \(32 \div 6\): \[ 3 \cdot 5 = 15 \] \[ 32 \div 6 \approx 5.33 \quad (\text{or } \frac{16}{3}) \]
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Rewrite the expression with these values: \[ -6 + 15 , _ , 4 + 5.33 \]
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Combine the values: \[ -6 + 15 = 9 \] So it becomes: \[ 9 , _ , 4 + 5.33 \]
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Now perform \(9 + 5.33 = 14.33\).
Now we have: \[ 14.33 , _ , 4 \]
Next, we need to check each operator (<, >, =) to see what makes sense:
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If we substitute < : \[ 14.33 < 4 \quad \text{(False)} \]
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If we substitute > : \[ 14.33 > 4 \quad \text{(True)} \]
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If we substitute = : \[ 14.33 = 4 \quad \text{(False)} \]
Thus, the operator that can be inserted to make the statement true is:
\[
\]