Absolute Value Equation

An absolute value equation is an equation in which the unknown variable appears inside an absolute value sign. The absolute value of a number is the distance of that number from zero on a number line, regardless of direction. In essence, it converts negative numbers to positive numbers. The absolute value of a number x is represented as |x|. An absolute value equation has the form |x| = a, where a is a positive constant or zero. To solve the equation, one must find all values of x that satisfy the condition that when the absolute value of x is taken, it equals a. This can yield two possible solutions: x = a and x = -a, since absolute value signifies distance on the number line, both the positive and negative distance from zero to a satisfy the equation.