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.
`380 xx 19 + 2 - 4 -: 2 = 14`

Options

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

Explanation

To solve the equation \( 380 \times 19 + 2 - 4 \div 2 = 14 \) and find the correct alternative by interchanging two signs, we will follow these steps:

### Step 1: Analyze the given equation
The equation is:
\[ 380 \times 19 + 2 - 4 \div 2 = 14 \]

### Step 2: Identify the operations and their order
According to the BODMAS/BIDMAS rule, we perform operations in the following order:
1. Brackets
2. Orders (i.e., powers and roots, etc.)
3. Division and Multiplication (from left to right)
4. Addition and Subtraction (from left to right)

### Step 3: Calculate the left-hand side of the equation
Let's calculate the left-hand side:
1. First, perform the multiplication:
\[ 380 \times 19 = 7220 \]
2. Next, perform the division:
\[ 4 \div 2 = 2 \]
3. Substitute these values back into the equation:
\[ 7220 + 2 - 2 = 7220 \]

Clearly, \( 7220 \neq 14 \), so the equation is incorrect.

### Step 4: Test the first option (interchanging multiplication with addition)
If we interchange multiplication with addition:
\[ 380 + 19 \times 2 - 4 \div 2 \]
1. Calculate:
- First, perform the multiplication:
\[ 19 \times 2 = 38 \]
- Then, perform the division:
\[ 4 \div 2 = 2 \]
- Substitute back:
\[ 380 + 38 - 2 = 416 \]
- Since \( 416 \neq 14 \), option 1 is incorrect.

### Step 5: Test the second option (interchanging multiplication with division)
If we interchange multiplication with division:
\[ 380 \div 19 + 2 - 4 \div 2 \]
1. Calculate:
- First, perform the division:
\[ 380 \div 19 = 20 \]
- Then, perform the division:
\[ 4 \div 2 = 2 \]
- Substitute back:
\[ 20 + 2 - 2 = 20 \]
- Since \( 20 \neq 14 \), option 2 is incorrect.

### Step 6: Test the third option (interchanging addition with subtraction)
If we interchange addition with subtraction:
\[ 380 \times 19 - 2 + 4 \div 2 \]
1. Calculate:
- First, perform the multiplication:
\[ 380 \times 19 = 7220 \]
- Then, perform the division:
\[ 4 \div 2 = 2 \]
- Substitute back:
\[ 7220 - 2 + 2 = 7220 \]
- Since \( 7220 \neq 14 \), option 3 is incorrect.

### Step 7: Test the fourth option (interchanging subtraction with division)
If we interchange subtraction with division:
\[ 380 \times 19 + 2 \div 4 - 2 \]
1. Calculate:
- First, perform the multiplication:
\[ 380 \times 19 = 7220 \]
- Then, perform the division:
\[ 2 \div 4 = 0.5 \]
- Substitute back:
\[ 7220 + 0.5 - 2 = 7218.5 \]
- Since \( 7218.5 \neq 14 \), option 4 is incorrect.

### Conclusion
After testing all options, the correct alternative is the second option where multiplication is interchanged with division, making the equation correct.