Question

\(3 - 2[5 - 7(3+2)] =\)

• A. -30
• B. -10
• C. 23
• D. 63
• E. 77

Hint:

Be very careful with negative signs, especially when subtracting a negative number, as in the final step: \(3 - (-60)\) becomes \(3 + 60\). This is a common source of errors.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This is an arithmetic problem that requires careful application of the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Step 2: Detailed Explanation:
We evaluate the expression step-by-step, starting from the innermost grouping symbols.
The expression is: \(3 - 2[5 - 7(3+2)]\)
1. Innermost Parentheses: First, calculate the sum inside the parentheses.
\[ 3 + 2 = 5 \]
The expression becomes: \(3 - 2[5 - 7(5)]\)
2. Brackets - Multiplication: Next, perform the multiplication inside the square brackets.
\[ 7(5) = 35 \]
The expression becomes: \(3 - 2[5 - 35]\)
3. Brackets - Subtraction: Now, perform the subtraction inside the square brackets.
\[ 5 - 35 = -30 \]
The expression becomes: \(3 - 2[-30]\)
4. Multiplication: Perform the multiplication of -2 and -30.
\[ -2 \times -30 = 60 \]
The expression becomes: \(3 + 60\)
5. Addition: Finally, perform the addition.
\[ 3 + 60 = 63 \]
Step 3: Final Answer:
The value of the expression is 63.