Question

hich 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 inequalities is true, we need to calculate the absolute values involved in each inequality.

1. \( | -687 | = 687 \)
2. \( | 786 | = 786 \)
3. \( | -786 | = 786 \)
4. \( | 687 | = 687 \)

Now, we will evaluate each inequality step by step:

**A**: \( | -687 | > | 786 | \)
- This becomes \( 687 > 786 \) which is **false**.

**B**: \( | -687 | > | -786 | \)
- This becomes \( 687 > 786 \) which is **false**.

**C**: \( | 687 | > | 786 | \)
- This becomes \( 687 > 786 \) which is **false**.

**D**: \( | -786 | > | 687 | \)
- This becomes \( 786 > 687 \) which is **true**.

Therefore, the true inequality is:

**D**: \( | -786 | > | 687 | \)