Two integers A and B are graphed on a number line. If A is less than B, is |A| always less than |B|?
no
use and example,
let A = -5 and B = -10
clearly B < A
but |B| > |A|
It is only true if both A and B ≥ 0
Thank you! I understand it now :)
To answer this question, let's first understand the concept of absolute values and the number line.
The absolute value of a number is its distance from zero on the number line. No matter whether a number is positive or negative, its absolute value is always positive or zero.
Now, let's consider two integers A and B on a number line. If A is less than B, it means that A is to the left of B on the number line.
To determine whether |A| is always less than |B| when A is less than B, we need to consider the possible cases:
1. A and B are both positive integers: If A is to the left of B, it means that |A| is smaller than B, but since |A| and |B| are the distance from zero, both will be the same, so |A| is not necessarily less than |B|.
2. A and B are both negative integers: If A is to the left of B, it means that |A| is greater than B, but since |A| and |B| are the distance from zero, both will be the same, so |A| is not necessarily less than |B|.
3. A is positive and B is negative: In this case, A is always to the left of B. When we take the absolute values of A and B, |A| will be equal to A (since it is already positive), and |B| will be equal to -B (since the negative sign is removed). Since A is less than 0 and -B is greater than 0, it means that |A| is always less than |B|.
Therefore, the statement "if A is less than B, |A| is always less than |B|" is true only when A is a positive integer and B is a negative integer. In other cases (both positive or both negative), |A| is not necessarily less than |B|.