In each of the following questions, an equation becomes incorrect due to the interchange of two signs. One of the four alternatives under it specifies the interchange of signs in the equation, which when made will make the equation correct. Find the correct alternative.
`2 xx 3 + 6 - 12 -: 4 = 17`

Options

A. `xx` and +
B. `+` and -
C. `+` and `-:`
D. `-` and `-:`

Explanation

To solve the equation \(2 \times 3 + 6 - 12 \div 4 = 17\) and determine which signs need to be interchanged to make it correct, we will follow these steps:

### Step 1: Analyze the given equation
The original equation is:
\[ 2 \times 3 + 6 - 12 \div 4 = 17 \]
We need to check if this equation is true or false.

### Step 2: Perform operations according to BODMAS/BIDMAS rules
According to the BODMAS/BIDMAS rules, we perform division and multiplication before addition and subtraction.

1. **Division**: Calculate \(12 \div 4\):
\[ 12 \div 4 = 3 \]

2. **Substituting back into the equation**:
\[ 2 \times 3 + 6 - 3 = 17 \]

3. **Multiplication**: Calculate \(2 \times 3\):
\[ 2 \times 3 = 6 \]

4. **Substituting back into the equation**:
\[ 6 + 6 - 3 = 17 \]

5. **Addition and Subtraction**:
- First, perform the addition:
\[ 6 + 6 = 12 \]
- Then, perform the subtraction:
\[ 12 - 3 = 9 \]

### Step 3: Conclusion of the original equation
The left-hand side evaluates to \(9\), which does not equal \(17\). Therefore, the original equation is incorrect.

### Step 4: Identify the signs to interchange
We need to find an option that, when interchanged, will make the equation correct. Let's check the first option, which suggests interchanging multiplication and addition.

### Step 5: Interchange multiplication and addition
If we interchange \( \times \) and \( + \), the equation becomes:
\[ 2 + 3 \times 6 - 12 \div 4 \]

### Step 6: Perform operations again
1. **Division**: Calculate \(12 \div 4\):
\[ 12 \div 4 = 3 \]

2. **Substituting back into the equation**:
\[ 2 + 3 \times 6 - 3 \]

3. **Multiplication**: Calculate \(3 \times 6\):
\[ 3 \times 6 = 18 \]

4. **Substituting back into the equation**:
\[ 2 + 18 - 3 \]

5. **Addition and Subtraction**:
- First, perform the addition:
\[ 2 + 18 = 20 \]
- Then, perform the subtraction:
\[ 20 - 3 = 17 \]

### Step 7: Final conclusion
The left-hand side now evaluates to \(17\), which matches the right-hand side. Thus, the correct option is to interchange multiplication and addition.

### Summary of the solution:
The correct alternative is to interchange the multiplication sign with the addition sign.

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