Question

Explain why $8<x<2$ has no solution.

   Explain why $8<x<2$ has no solution.

College Algebra Essentials

College Algebra Essentials

Julie Miller 1st Edition

Chapter 1, Problem 100

Instant Answer

Solved by Expert James Kiss

09/12/2023

Step 1

This inequality is saying that $x$ is greater than $8$ and at the same time, $x$ is less than $2$. Show more…

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Explain why $8<x<2$ has no solution.

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Key Concepts

Ordered Property of Real Numbers

In the real numbers, every pair of numbers is comparable, meaning for any two distinct numbers, one must be less than the other. This property implies that when an inequality incorrectly orders constants—for example, requiring a number to be greater than a larger number and less than a smaller one—no number can satisfy the condition.

Contradiction in Inequalities

An inequality such as 8 < x < 2 sets up a contradictory condition by demanding that x be greater than 8 and at the same time less than 2. Since 8 is already greater than 2, there is no value of x that can simultaneously satisfy both parts of the inequality, resulting in no solution.

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