Two numbers A and B are graphed on a number line. Is it always,sometimes, or never true that A-B < A+B?
sometimes
4-2 < 4+2
4-(-2) > 4+(-2)
4-0 = 4+0
It is always true that A-B < A+B when two numbers A and B are graphed on a number line. To understand why, let's break it down step by step:
1. Let's start by assuming that A and B are any two numbers on a number line.
2. The expression A-B represents the difference between A and B. This means that it calculates how far apart A and B are from each other on the number line.
3. On the other hand, the expression A+B represents the sum of A and B. This means that it calculates the total distance when we move from A to B.
4. Since we know that the difference between two numbers is always smaller than their sum, it follows that A-B < A+B.
Therefore, it is always true that A-B < A+B when two numbers A and B are graphed on a number line.
To determine whether it is always, sometimes, or never true that A - B < A + B, let's analyze the question.
We can start by considering different scenarios:
1. A and B are positive numbers:
- In this case, both A - B and A + B are positive. Therefore, it is always true that A - B < A + B.
2. A and B are negative numbers:
- In this case, both A - B and A + B are negative. Therefore, it is always true that A - B < A + B.
3. One of A or B is negative, and the other is positive:
- Depending on the values of A and B, A - B can be less than, equal to, or greater than A + B. Therefore, it is sometimes true that A - B < A + B.
Given these scenarios, we can conclude that it is sometimes true that A - B < A + B.