To determine which symbol can replace the question mark to make the inequality \(2x , ? , 20\) true for the solutions \(x = 10\), \(x = 11\), and \(x = 12\), we will evaluate \(2x\) for these values of \(x\) and check the relationship to \(20\).
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For \(x = 10\): \[ 2x = 2(10) = 20 \]
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For \(x = 11\): \[ 2x = 2(11) = 22 \]
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For \(x = 12\): \[ 2x = 2(12) = 24 \]
Now we check what kind of inequality can hold:
- For \(x = 10\), \(2x = 20\). This means \(2x\) is equal to \(20\).
- For \(x = 11\), \(2x = 22\). This means \(2x\) is greater than \(20\).
- For \(x = 12\), \(2x = 24\). This means \(2x\) is also greater than \(20\).
The values of \(2x\) for \(x = 10\), \(11\), and \(12\) suggest that the appropriate symbol to replace the question mark is \(\geq\) (greater than or equal to).
Thus, the inequality is: \[ 2x \geq 20 \]
This is true for \(x = 10\), \(11\), and \(12\).