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.
`56 -: 7 xx 2 + 8-1 = 9`

Options

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

Explanation

To solve the equation \( 56 -: 7 \times 2 + 8 - 1 = 9 \) and find the correct alternative by interchanging two signs, we will follow these steps:

### Step 1: Understand the Original Equation
The original equation is:
\[ 56 \div 7 \times 2 + 8 - 1 = 9 \]
We need to check which interchange of signs makes this equation true.

### Step 2: Apply BODMAS Rule
According to the BODMAS rule, we perform operations in the following order: Brackets, Orders (i.e., powers and roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

### Step 3: Evaluate the Original Equation
Let's evaluate the left-hand side of the equation step by step:
1. **Division**: \( 56 \div 7 = 8 \)
2. **Multiplication**: \( 8 \times 2 = 16 \)
3. **Addition**: \( 16 + 8 = 24 \)
4. **Subtraction**: \( 24 - 1 = 23 \)

So, the left-hand side evaluates to \( 23 \), which does not equal \( 9 \).

### Step 4: Check Each Option for Interchanging Signs
We will check each option to see which one makes the equation true.

#### Option 1: Interchange Multiplication and Subtraction
Change \( \times \) to \( - \) and \( - \) to \( \times \):
\[ 56 \div 7 - 2 + 8 \times 1 \]
1. **Division**: \( 56 \div 7 = 8 \)
2. **Subtraction**: \( 8 - 2 = 6 \)
3. **Multiplication**: \( 8 \times 1 = 8 \)
4. **Addition**: \( 6 + 8 = 14 \)

Result: \( 14 \neq 9 \) (Option 1 is incorrect)

#### Option 2: Interchange Division and Multiplication
Change \( \div \) to \( \times \) and \( \times \) to \( \div \):
\[ 56 \times 7 \div 2 + 8 - 1 \]
1. **Multiplication**: \( 56 \times 7 = 392 \)
2. **Division**: \( 392 \div 2 = 196 \)
3. **Addition**: \( 196 + 8 = 204 \)
4. **Subtraction**: \( 204 - 1 = 203 \)

Result: \( 203 \neq 9 \) (Option 2 is incorrect)

#### Option 3: Interchange Addition and Subtraction
Change \( + \) to \( - \) and \( - \) to \( + \):
\[ 56 \div 7 \times 2 - 8 + 1 \]
1. **Division**: \( 56 \div 7 = 8 \)
2. **Multiplication**: \( 8 \times 2 = 16 \)
3. **Subtraction**: \( 16 - 8 = 8 \)
4. **Addition**: \( 8 + 1 = 9 \)

Result: \( 9 = 9 \) (Option 3 is correct)

#### Option 4: Interchange Addition and Division
This option is not checked because Option 3 is already correct.

### Final Answer
The correct alternative is **Option 3**.