Is the comparison |12| > |−13| the same as 12 > −13 ?

Answer 1

No, the comparison \( |12| > |−13| \) is not the same as \( 12 > −13 \).

Let's break it down:

1. **Absolute Value Comparison \( |12| > |−13| \):**
- The absolute value of a number is its distance from zero on the number line, regardless of direction.
- \( |12| \) is 12.
- \( |−13| \) is 13.
- Therefore, the comparison \( 12 > 13 \) (from the absolute values) is false.

2. **Direct Number Comparison \( 12 > −13 \):**
- Here, you are comparing the numbers without considering their absolute values.
- 12 is indeed greater than −13.
- Therefore, this comparison is true.

So, \( |12| > |−13| \) is false, while \( 12 > −13 \) is true. They are different comparisons and yield different results.