Question - Solving Inequality Involving Absolute Value
mathsolving inequalityinequality solutionabsolute value inequalitycases in absolute value inequality
Solution:
This inequality involves an absolute value. To solve it, you need to consider two cases because the absolute value of an expression represents its distance from zero on the number line, which could be either positive or negative.The inequality is $$10 > |q - 10|$$.Case 1: $$q - 10$$ is positive, which means that $$q$$ is greater than 10. \[q - 10 < 10\]\[q < 20\]Case 2: $$q - 10$$ is negative, which means that $$q$$ is less than 10. When you remove the absolute value, you must also flip the inequality sign.\[ -(q - 10) < 10\]\[-q + 10 < 10\]\[-q < 0\]\[q > 0\]So, $$q$$ must be greater than 0 and less than 20. Putting both cases together, you get the solution:\[0 < q < 20\]The values of $$q$$ that satisfy the inequality are all the numbers between 0 and 20, not including 0 and 20 themselves.
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