To simplify the expression \( 4 + [5(10 + 2 - 8)] \div 5 \times 3 \), we will follow the order of operations, often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Let's break it down step-by-step.
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Evaluate the Parentheses: First, solve inside the brackets: \[ 10 + 2 - 8 \] First, add \( 10 + 2 = 12 \). Then, subtract \( 12 - 8 = 4 \). Now, replace this back into the expression: \[ 4 + [5(4)] \div 5 \times 3 \]
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Multiply inside the brackets: Now we perform the multiplication: \[ 5(4) = 20 \] Substitute this value back into the expression: \[ 4 + [20] \div 5 \times 3 \]
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Evaluate the Division: Next, we need to perform the division: \[ 20 \div 5 = 4 \] Now, replace this value back into the expression: \[ 4 + 4 \times 3 \]
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Perform the Multiplication: Next, multiply: \[ 4 \times 3 = 12 \] Substitute this back into the expression: \[ 4 + 12 \]
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Perform the Addition: Finally, add the remaining numbers: \[ 4 + 12 = 16 \]
Thus, the simplified expression is: \[ \boxed{16} \]