The number m satisfies the relationship m < 0. Write an inequality expressing the relationship between -m and 0. Explain your reasoning.
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m < 0
subtract m from both sides, and you have
0 < -m
To express the relationship between -m and 0, we need to consider the two scenarios.
1. If m < 0:
In this case, -m will be positive. When we take the opposite of a negative number, it becomes positive. So, -m > 0 represents the relationship between -m and 0 when m < 0.
2. If m > 0 or m = 0:
In this case, -m will be negative or zero. When we take the opposite of a positive number or zero, it becomes negative or zero respectively. So, -m ≤ 0 represents the relationship between -m and 0 when m > 0 or m = 0.
In summary, the inequality expressing the relationship between -m and 0 is:
- m > 0 when m < 0,
- m ≤ 0 when m > 0 or m = 0.
To write an inequality expressing the relationship between -m and 0, we need to consider the relationship between m and 0.
Given that m < 0, it means that m is a negative number. So, -m would be the opposite of m, which means -m would be a positive number.
To express the relationship between -m and 0, we need to state that -m is greater than 0. We can write this as:
-m > 0
The reasoning behind this inequality is that since m is negative, when we take the negative of m, i.e., -m, it becomes positive. Since we know that 0 is not negative, -m must be greater than 0 to represent the relationship between -m and 0.