To simplify the expression \( 4(11 + 7) \div (7 - 5) \), let's follow the order of operations (parentheses, exponents, multiplication and division from left to right, addition and subtraction from left to right):
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Calculate the expressions inside the parentheses: \[ 11 + 7 = 18 \] \[ 7 - 5 = 2 \]
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Substitute these values back into the expression: \[ 4(18) \div (2) \]
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Perform the multiplication: \[ 4 \times 18 = 72 \]
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Now, divide by 2: \[ 72 \div 2 = 36 \]
Thus, the simplified expression is \( 36 \).
So the answer is \( \boxed{36} \).
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