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Absolute value equations and inequalities math. Let s first return to the original definition of absolute value. The reference used is the college algebra and trigonometry book by lial et al. For example 3 3 and 3 3. That is we have.
Whereas the inequality left x right 2 represents the distance between x and 0 that is greater than 2. This means that their absolute values will both be 2. The inequality left x right 2 represents the distance between x and 0 that is less than 2. Because if it s less than negative 21 when you take its absolute value it s going to be more than 21 away from 0.
Recall that the absolute value of a real number a denoted a is defined as the distance between zero the origin and the graph of that real number on the number line. X is the distance of x from zero for instance both 2 and 2 are two units from zero as you can see in the image below. Solving absolute value equations graphing absolute value functions solving absolute value inequalities our mission is to provide a free world class education to anyone anywhere. In addition the absolute value of a real number can be defined algebraically as a piecewise function.
An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative. Solving an absolute value equation.
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