Absolute value of X can be treated as a distance on the number line from zero to X, so it has no sign (or it's always positive, never negative). For example [tex]|X|=X[/tex] but also: [tex]|-X|=X[/tex]
That means that the absolute value of a rational number and its opposite may only be equal, if the rational number is lower than 0 (see the example above).
