To solve the expression \( 21 \div 3 + 4 + |2 - 3| \), we can follow the order of operations (PEMDAS/BODMAS):
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Absolute Value Calculation: \[ |2 - 3| = |-1| = 1 \]
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Division: \[ 21 \div 3 = 7 \]
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Addition: Now we add the results: \[ 7 + 4 + 1 \]
First, \( 7 + 4 = 11 \), and then: \[ 11 + 1 = 12 \]
So, the final answer is \( 12 \).
Thus, the answer is: 12