46-[27-{32-(17-?)}]=58

Options

A. -24
B. -14
C. 14
D. 24

Answer

To solve the equation \( 46 - [27 - \{32 - (17 - ?)\}] = 58 \), 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)).

### Step-by-Step Solution:

1. **Start with the innermost parentheses**:
\[ 17 - ? \]
Let's denote this as \( x \). So, we have:
\[ x = 17 - ? \]

2. **Substitute \( x \) into the next operation**:
\[ 32 - x = 32 - (17 - ?) = 32 - 17 + ? = 15 + ? \]

3. **Now substitute this result into the curly brackets**:
\[ 27 - (15 + ?) = 27 - 15 - ? = 12 - ? \]

4. **Now substitute this into the square brackets**:
\[ 46 - [12 - ?] = 46 - 12 + ? = 34 + ? \]

5. **Set the equation equal to 58**:
\[ 34 + ? = 58 \]

6. **Now, solve for \( ? \)**:
\[ ? = 58 - 34 = 24 \]

### Final Answer:
The value of \( ? \) is \( 24 \).