To simplify the expression \((23 - 12.13) - (166.4 + 2)\), we will first perform the operations inside the parentheses and then simplify the overall expression.
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Start with \((23 - 12.13)\): \[ 23 - 12.13 = 10.87 \]
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Next, simplify \((166.4 + 2)\): \[ 166.4 + 2 = 168.4 \]
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Now substitute these results back into the main expression: \[ (23 - 12.13) - (166.4 + 2) = 10.87 - 168.4 \]
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Now calculate \(10.87 - 168.4\): To perform the subtraction, we can convert \(10.87\) to a form with matching decimal places: \[ 10.87 - 168.40 = 10.87 - 168.40 = -157.53 \]
So, the simplified expression is: \[ \boxed{-157.53} \]