Which of the following statements is true ?

Options

A. `|10-4|=|10|+-4|`
B. Additive inverse of -5 is 5
C. `-1` lies on the right of 0 on the number line
D. `-7` is greater than `-3`.

Answer

To determine which of the given statements is true, let's analyze each statement one by one.

**Step 1: Analyze Statement 1**
- Statement: The absolute function |10 - 4| = |10 + (-4)|.
- Calculation:
- |10 - 4| = |6| = 6
- |10 + (-4)| = |10 - 4| = |6| = 6
- Conclusion: This statement is true.

**Step 2: Analyze Statement 2**
- Statement: The additive inverse of -5 is 5.
- Definition: The additive inverse of a number is the number that, when added to the original number, results in 0.
- Calculation:
- Additive inverse of -5 is 5 because -5 + 5 = 0.
- Conclusion: This statement is true.

**Step 3: Analyze Statement 3**
- Statement: -1 lies on the right of 0 on the number line.
- Number line position:
- 0 is at the center, -1 is to the left of 0.
- Conclusion: This statement is false.

**Step 4: Analyze Statement 4**
- Statement: -7 is greater than -3.
- Number line position:
- -3 is to the right of -7 on the number line.
- Conclusion: This statement is false.

**Final Conclusion:**
- The true statements are:
- Statement 1: |10 - 4| = |10 + (-4)| is true.
- Statement 2: The additive inverse of -5 is 5 is also true.
- Therefore, the correct answer is that both Statement 1 and Statement 2 are true.