To solve the expression \( 42 - (7 + 14) \div 7 \times 4 \), we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
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Start by solving the expression inside the parentheses: \[ 7 + 14 = 21 \] Now the expression becomes: \[ 42 - 21 \div 7 \times 4 \]
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Next, perform the division: \[ 21 \div 7 = 3 \] Now the expression updates to: \[ 42 - 3 \times 4 \]
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Then, perform the multiplication: \[ 3 \times 4 = 12 \] Now the expression is: \[ 42 - 12 \]
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Finally, perform the subtraction: \[ 42 - 12 = 30 \]
Thus, the value of the expression \( 42 - (7 + 14) \div 7 \times 4 \) is \(\boxed{30}\).