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Absolute Value Inequalities - Problem 7 267 views

As always, when you are solving an absolute value equation or inequality, your first goal is to isolate the absolute value expression. From there with inequalities, if the constant value on the other side of the inequality is negative, then you'll have a special case. If your isolated absolute value is greater than (or greater than or equal to) a negative value, then the solution is all real numbers: any x value will give a positive distance from zero, which will always be greater than a negative value. If your isolated absolute value is less than (or less than or equal to) a negative value, then the solution is "no solution," because positive distance could never be less than a negative value. It is sometimes helpful to look at these graphically as well as algebraically.

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