An absolute personal equation is the difference between an observed value and a standard value assumed as being true.
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Mainly that somewhere in the equation there is an absolute value, usually of an expression that involves the variable.
It is an equation used to anwer an absolute value inequality.
For example: | x | = -1 Or any other equation where the absolute value of any expression is negative. This doesn't have a solution, because the absolute number of any expression is always positive, or zero, never negative.
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You know if an equation is linear if it is a straight line. You can also know if the equation is y = mx + b where there are no absolute values nor exponents.