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Chapter 1: Problem 140

Explain why \(|x|<-4\) has no solution.

Short Answer

Expert verified
The expression \(|x|<-4\) has no solution because the absolute value of a number is non-negative, meaning it can never be less than a negative number.

Step by step solution

01

Understanding the Absolute Value

Firstly, to analyse the equation \(|x|<-4\), it's important to understand what an absolute value signifies. Absolute value, denoted by \(|x|\), of a number refers to the distance of that number from zero on the number line, regardless of the direction. Therefore, it is always non-negative.
02

Analyzing the Combining of Absolute Value and Negation

Next, consider the requirement that the absolute value of \(x\) is less than -4. Because the absolute value of a number is always non-negative, it cannot be less than any negative number, including -4.
03

Summarizing the Conclusion

From the above exploration, it is clarified that an absolute value can't be less than a negative number. Therefore, the mathematical expression \(|x|<-4\) has no solution in the realm of real numbers.

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