To determine which symbol makes the inequality \(2x , ? , 20\) true for the solutions 10, 11, and 12, we can evaluate it for each solution.
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For \( x = 10 \): \[ 2 \times 10 = 20 \] We need to check whether \(20\) satisfies the inequality.
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For \( x = 11 \): \[ 2 \times 11 = 22 \] Now check if \(22\) satisfies the inequality.
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For \( x = 12 \): \[ 2 \times 12 = 24 \] Finally, check if \(24\) satisfies the inequality.
Now, we analyze the possible symbols:
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If we use \( < \):
- \( 20 < 20 \) is false (does not work for \( x = 10\))
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If we use \( > \):
- \( 20 > 20 \) is false (does not work for \( x = 10\))
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If we use \( \leq \):
- \( 20 \leq 20 \) is true (works for \( x = 10\)),
- \( 22 \leq 20 \) is false (does not work for \( x = 11\)),
- \( 24 \leq 20 \) is false (does not work for \( x = 12\))
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If we use \( \geq \):
- \( 20 \geq 20 \) is true (works for \( x = 10\)),
- \( 22 \geq 20 \) is true (works for \( x = 11\)),
- \( 24 \geq 20 \) is true (works for \( x = 12\))
Thus, the symbol that makes the inequality true for all the provided solutions (10, 11, and 12) is \( \geq \).
So, the correct symbol to replace the question mark is:
\[ \geq \]