To solve the expression \(|7(-3) + 2(4)|\), we will start by evaluating the expression inside the absolute value.
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Calculate \(7(-3)\): \[ 7 \times -3 = -21 \]
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Calculate \(2(4)\): \[ 2 \times 4 = 8 \]
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Now, substitute these values back into the expression: \[ -21 + 8 \]
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Perform the addition: \[ -21 + 8 = -13 \]
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Now apply the absolute value: \[ |-13| = 13 \]
So, the final result is: \[ \boxed{13} \]