Question

A number and it's absolute value are equal. If you subtract 2 from the number , the new number and it's absolute value are not equal. What do you know about the number? What is the possible number that satisfies these condition?

Answer 1

For all the non-negative numbers, the absolute value is always equal to the actual number.

If "x" is any non-negative number, then:

|x| = x

For all negative numbers, the absolute value is equal to -1 multiplied to that number.

If x is any negative number, then:

|x| = -x 

So, if after subtracting 2 the number is not anymore equal to it absolute value, this means when 2 is subtracted the number changes from positive to negative.

Only one such number exists that changes from positive to negative on subtraction of 2 and that number if 1.

Absolute value of 1 is 1.
When 2 is subtracted from 1, the result is -1. The absolute value of -1 is also 1. So the absolute value is no longer equal to the original value.

The possible number that satisfies the given condition is 1. 

Answer 2

If the number and its absolute value are equal, then that number is positive.

If you subtract 2, and then the new number and it's absolute value are not equal it means, that the new number is a negative number.

Our original number could be 1.

1 = |1|

1 - 2 = -1

$-1 \neq |-1| \\ -1 \neq 1$

The number 1 satisfies those conditions.