Explain why - 5 > y > - 2 has no solution.

Name: Problem 41, Chapter 1: Intermediate Algebra
Uploaded: 2020-06-21T12:31:49-08:00
Duration: 33 s
Channel: Ankit Gupta
Description: Explain why - 5 > y > - 2 has no solution.

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Key Concepts

Compound Inequalities

A compound inequality involves two inequality comparisons combined together, which restricts the values of a variable to lie between the bounds specified. When solving compound inequalities, both parts must be satisfied simultaneously. If the structure of the inequality is set up wrongly such that the restrictions contradict one another, then there are no values that can satisfy both conditions at the same time.

Order of Real Numbers

The concept of the order of real numbers is key to understanding why the inequality -5 > y > -2 has no solution. On the number line, -5 is to the left of -2, meaning it is actually less than -2. An inequality that tries to place y between -5 and -2 while having -5 > y (so y is less than -5) and y > -2 (so y is greater than -2) creates a paradox because the lower bound is greater than the upper bound.

Logical Contradiction

The logical contradiction arises when the boundaries implied by the inequality are inconsistent. In any valid interval, the left endpoint must be less than the right endpoint. Here, stating -5 > y > -2 implies that the lower bound (-5) is larger than the upper bound (-2). This inherent contradiction makes it impossible for any real number to satisfy both parts of the compound inequality simultaneously.

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