In each of the following questions if the interchanges are made in signs and numbers, which one of the four equations would be correct?
Given interchanges: Signs: - and + and numbers 8 and 4

Options

A. `4 + 8 -1 = 5`
B. `4 - 8 + 5 =9`
C. `4 + 8-5 = 10`
D. `4 - 8 + 12 = 1`

Explanation

To solve the problem, we need to analyze the given equations and apply the specified interchanges:

1. Interchange the signs: - becomes + and + becomes -.
2. Interchange the numbers: 8 becomes 4 and 4 becomes 8.

Let's go through each option step by step:

**Option 1: 4 + 8 - 1 = 8 + 4 - 5**

1. Start with the left side:
- Original: 4 + 8 - 1
- Interchanging: 4 becomes 8, + becomes -, 8 becomes 4, and - remains as is.
- New left side: 8 - 4 - 1 = 8 - 4 - 1 = 4 - 1 = 3.

2. Now for the right side:
- Original: 8 + 4 - 5
- Interchanging: 8 becomes 4, + becomes -, 4 becomes 8, and - remains as is.
- New right side: 4 - 8 - 5 = 4 - 8 - 5 = -4 - 5 = -9.

3. Check if the new left side equals the new right side:
- 3 ≠ -9 (not equal).

**Option 2: 4 - 8 + 1 = 8 - 4 + 5**

1. Start with the left side:
- Original: 4 - 8 + 1
- Interchanging: 4 becomes 8, - becomes +, 8 becomes 4, and + remains as is.
- New left side: 8 + 4 + 1 = 8 + 4 + 1 = 12 + 1 = 13.

2. Now for the right side:
- Original: 8 - 4 + 5
- Interchanging: 8 becomes 4, - becomes +, 4 becomes 8, and + remains as is.
- New right side: 4 + 8 + 5 = 4 + 8 + 5 = 12 + 5 = 17.

3. Check if the new left side equals the new right side:
- 13 ≠ 17 (not equal).

**Option 3: 4 + 8 - 5 = 8 + 4 - 10**

1. Start with the left side:
- Original: 4 + 8 - 5
- Interchanging: 4 becomes 8, + becomes -, 8 becomes 4, and - remains as is.
- New left side: 8 - 4 - 5 = 8 - 4 - 5 = 4 - 5 = -1.

2. Now for the right side:
- Original: 8 + 4 - 10
- Interchanging: 8 becomes 4, + becomes -, 4 becomes 8, and - remains as is.
- New right side: 4 - 8 - 10 = 4 - 8 - 10 = -4 - 10 = -14.

3. Check if the new left side equals the new right side:
- -1 ≠ -14 (not equal).

**Option 4: 4 - 8 + 12 = 8 + 4 - 12**

1. Start with the left side:
- Original: 4 - 8 + 12
- Interchanging: 4 becomes 8, - becomes +, 8 becomes 4, and + remains as is.
- New left side: 8 + 4 + 12 = 8 + 4 + 12 = 12 + 12 = 24.

2. Now for the right side:
- Original: 8 + 4 - 12
- Interchanging: 8 becomes 4, + becomes -, 4 becomes 8, and - remains as is.
- New right side: 4 - 8 - 12 = 4 - 8 - 12 = -4 - 12 = -16.

3. Check if the new left side equals the new right side:
- 24 ≠ -16 (not equal).

After checking all options, we find that none of the equations are equal after interchanging the signs and numbers. Therefore, none of the options are correct based on the given interchanges.