An absolute value equation is an equation that contains the absolute value of a variable expression. Equations of the type where can be solved by thinking of the absolute value of a number as the distance between and on the number line. For example, are all values of which are units away from
As there are two points on the number line that fulfill this requirement, there are two solutions to the equation namely and
The absolute value equation has two solutions. Equations of the same type, will have or solutions, depending on More complex absolute value equations may have more than solutions.
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When solving absolute value equations algebraically, it is necessary to take into consideration that the absolute value of both a negative number and a positive yields a positive. One possible strategy is to, when removing the absolute value, split the equation into two cases: one case where the expression inside the absolute value is negative and one where it is positive.