Find the values for which the statement is true. x=|-x|

Answer 1

Observe that the right hand side must be nonnegative, regardless of the value of x. Thus the left hand side must also be nonnegative, so x must be greater than or equal to 0. Now, given any positive value for the left hand side, if we put that value into the right hand side, the absolute value will remove the negative and return that same value that we input. Thus the expression holds for all x greater than or equal to 0.