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Chapter 1: Problem 70

Solve each absolute value inequality. $$|x|>5$$

Short Answer

Expert verified
The solution of the inequality \(|x|>5\) is \(x \in (-\infty, -5)\) or \(x \in (5, \infty)\).

Step by step solution

01

Define the Inequality

First define the inequality without absolute value: \(|x|>5\) which can also be written as \(x > 5\) or \(x < -5\)
02

Solve for x in both cases

Starting with the positive scenario: \(x > 5\). This indicates that x can be any value greater than 5. For the negative scenario: \(x < -5\). Here, x can be any value less than -5.
03

Conclusion

Combine the solutions from both the positive and negative scenarios. This concludes that x can either be less than -5 or greater than 5. Therefore, the set of all possible solutions will be \(x \in (-\infty, -5)\) or \(x \in (5, \infty)\). This is an absolute value inequality and will have two solutions

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