Absolute value equations - FREE Math Worksheets When faced with an absolute value equation, we need to correctly utilize the definition of absolute value. Definition: Let x be some variable or algebraic expression. Then. | x | = { − x, i f x < 0 x, i f x ⩾ 0. We can state this in the form of an equation as. | x | = a ⇔ x = − a or x = a. That is, if x is a negative number, then the ...