Question

Which pair of statements is true?

1. 15 > -9 and 1-9| > |15||
2. -15 < -9 and 1–9| < |--15)
3. -15 < 9 and 1–15] < 9
4. -15 > -9 and |–15> 1-9|

Answer 1

The correct pair of statements is the second option: -15 < -9 and |1-9| < |-15|, as both inequalities in this option are true.

Step-by-step explanation:

The question asks us to find which pair of statements is true, comparing inequalities and absolute values:

1. 15 > -9 and |1-9| > |15|
2. -15 < -9 and |1−9| < |-−15|
3. -15 < 9 and |1−15| < 9
4. -15 > -9 and |−15| > |1-9|

Let's evaluate these one by one:

• 15 is indeed greater than -9, but the second part of the statement is incorrect since |1 - 9| equals 8, which is not greater than |15|, which equals 15.
• -15 is indeed less than -9, and |1−9|, which equals 8, is also less than |-15|, which equals 15. This pair of statements is true.
• -15 is less than 9, which is true. However, |1−15| equals 14, which is not less than 9.
• -15 is not greater than -9, so the entire pair of statements is false.

Hence, the correct answer is the second pair of statements:

-15 < -9 and |1-9| < |-15|