|-x|= x for which value of x will the equality be valid?

Question

will the equality be valid if x is greater than or equal to 0

and invalid if x is less than 0?

-how do I explain this?

Answer 1

 

The rule for absolute value is 

 

|N| =    N if N>0,

           -N if N<0,

           0 if N=0

 

 

The equality holds for x=0

 

If x>0, then -x<0.

So |-x| = -(-x) = x and the equality holds.

 

If x<0, then -x>0.

|-x|=-x > 0 and the equality does not hold.

 

So the equality is valid for all x>=0

Answer 2

The absolute value of an expression is the non-negative (that is either 0 or positive) value of the expression without the sign.

 

For this problem, the absolute value of the expression (-x) must equal x (since x appears on the right side of the equation. This means that x is greater than or equal to 0. Thus, the equality is valid for all values of x greater than or equal to 9.

 

However, for negative values of x, the expression (-x) is positive. In this case, (-x) does not equal (x) so the equality |-x|=x is not valid.