Question

Which of the following inequalities is true?
A
∣−687∣>∣−786∣\left| -687\right| >\left| -786\right|∣−687∣>∣−786∣
B
∣−687∣>∣786∣\left| -687\right| >\left| 786\right|∣−687∣>∣786∣
C
∣687∣>∣786∣\left| 687\right| >\left| 786\right|∣687∣>∣786∣
D
∣−786∣>∣687∣\left| -786\right| >\left| 687\right|∣−786∣>∣687∣

Answer 1

To determine which of the given inequalities is true, we need to calculate the absolute values involved in each option.

1. **Option A: \(|-687| > |-786|\)**
- \(|-687| = 687\)
- \(|-786| = 786\)
- Therefore, \(687 > 786\) is false.

2. **Option B: \(|-687| > |786|\)**
- \(|-687| = 687\)
- \(|786| = 786\)
- Therefore, \(687 > 786\) is false.

3. **Option C: \(|687| > |786|\)**
- \(|687| = 687\)
- \(|786| = 786\)
- Therefore, \(687 > 786\) is false.

4. **Option D: \(|-786| > |687|\)**
- \(|-786| = 786\)
- \(|687| = 687\)
- Therefore, \(786 > 687\) is true.

The correct answer is **D**: \(|-786| > |687|\).