a number and its absolute value are equal.if you substract 2 from the number, the new number and its absolute value are not equal. what do you know about the number? what is a possible number that satisfies these conditions? Can you help answer these 2 questions? thanks
If x >= 0, |x| = x
If x < 0, |x| = -x
So, from what we have above,
x >= 0
x-2 < 0, or x < 2
So, 0 <= x < 2
Jerjjquau
To solve this problem, let's break it down step by step:
1. Let's assume the number is represented by the variable x.
2. The problem states that a number and its absolute value are equal, which means |x| = x.
3. We are also given that when we subtract 2 from the number, the new number and its absolute value are not equal.
This means, |x -2 | ≠ x - 2.
Now, let's analyze the problem further:
If |x| = x, it implies that x is a non-negative number (including zero) because the absolute value of any negative number is positive.
Now, let's consider |x - 2 | ≠ x - 2:
There are two possible scenarios:
1. If x - 2 is a positive number or zero, then its absolute value will be equal to x - 2. Therefore, |x - 2 | = x - 2. But, the problem states that it is not equal, so this scenario is not possible.
2. If x - 2 is a negative number, then its absolute value will be equal to -(x - 2) or -x + 2. Therefore, |x - 2 | = -x + 2. So, we can conclude that |x - 2 | ≠ x - 2 when x - 2 is negative.
Based on the above analysis, we can conclude that x - 2 is a negative number. Therefore, x - 2 < 0. Rearranging the inequality, we get:
x < 2
This means the number x must be less than 2.
Now, let's find a possible number that satisfies these conditions. To do this, we can choose any value less than 2 and substitute it into the equation. Let's choose x = 1 as an example:
|1| = 1, which satisfies the first condition.
|1 - 2| = |-1| = 1, which is not equal to 1 - 2.
Hence, the number x = 1 satisfies the conditions given.
To summarize:
- The number x must be less than 2.
- A possible number that satisfies these conditions is x = 1.