what are values of a and b, if any , where a|b-2|<0?
To find the values of a and b where the inequality a|b-2| < 0 is true, we need to understand the properties of absolute value and inequality.
First, let's review the properties of absolute value:
1. For any real number x, |x| is always greater than or equal to 0: |x| ≥ 0.
2. If x is a positive number, then |x| = x: |x| = x.
3. If x is a negative number, then |x| = -x: |x| = -x.
4. |0| = 0.
Now, let's analyze the inequality a|b-2| < 0:
Since the absolute value of any number is always greater than or equal to 0, it is not possible for the inequality to be true for any combination of a and b. This is because the left side of the inequality, a|b-2|, will always be greater than or equal to 0, while the right side of the inequality is less than 0.
Therefore, there are no values of a and b where the inequality a|b-2| < 0 is satisfied.