Question

1. kiran says that -2 < -5. do you agree with kiran? explain or show your reasoning.

4.

Explanation:

Step1: Recall number line order

On a number line, numbers increase from left to right. Negative numbers are to the left of 0, and as the magnitude of a negative number increases (becomes more negative), it is located further to the left.

Step2: Compare -2 and -5 on number line

-5 is to the left of -2 on the number line. So, in terms of inequality, a number to the left is less than a number to the right. So, \(-5 < -2\), which means \(-2 > -5\), not \(-2 < -5\).

Step3: Use absolute value to check

The absolute value of a number \(|x|\) is its distance from 0. \(|-2| = 2\) and \(|-5| = 5\). Since \(5>2\), \(-5\) is further from 0 (in the negative direction) than \(-2\). So, \(-5\) is less than \(-2\), so \(-2\) is not less than \(-5\).

Answer:

I do not agree with Kiran. On the number line, -5 is to the left of -2, so \(-5 < -2\) (or \(-2 > -5\)). Also, using absolute values, \(|-2| = 2\) and \(|-5| = 5\), and since a larger absolute value for a negative number means it is more negative (and thus smaller), \(-5\) is smaller than \(-2\), so \(-2\) is not less than \(-5\).