Is This an Example of Absolute Value Inequalities?

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Discussion Overview

The discussion revolves around the concept of absolute value inequalities, specifically examining the inequality | (4 - 5x)/2 | > 1. Participants explore the application of a theorem related to absolute values and engage in solving the inequality.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the inequality | (4 - 5x)/2 | > 1 and questions whether a specific theorem can be applied.
  • Another participant confirms that the theorem can be used and suggests two cases to consider: (4 - 5x)/2 > 1 and (4 - 5x)/2 < -1.
  • A third participant expresses confidence in continuing the solution process.
  • A later post reiterates the inequality and the theorem, providing a transformation of the inequality to |x - 4/5| > 2/5, suggesting that the solution becomes straightforward from this point.
  • One participant questions whether the original question is indeed classified as absolute value inequalities.

Areas of Agreement / Disagreement

Participants generally agree on the applicability of the theorem to the problem, but there are varying approaches to solving the inequality. The discussion remains open with no consensus on a single method or interpretation.

Contextual Notes

Some participants assume familiarity with the theorem and its implications, while others express uncertainty about the classification of the problem as an absolute value inequality.

mathdad
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Solve the inequality.

| (4 - 5x)/2 | > 1

Can I use the following theorem?

If a > 0, then | u | > a if and only if u < -a or u > a
 
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Yes, you can: either $$\frac{4- 5x}{2}> 1$$ or [math]\frac{4- 5x}{2}< -1[/math]. Continue, with either equation, by multiplying both sides by the positive number, 2.
 
I can take it from here.
 
RTCNTC said:
Solve the inequality.

| (4 - 5x)/2 | > 1

Can I use the following theorem?

If a > 0, then | u | > a if and only if u < -a or u > a

We are given:

$$\left|\frac{4-5x}{2}\right|>1$$

Multiply through by 2/5:

$$\left|x-\frac{4}{5}\right|>\frac{2}{5}$$

Now the solution is easy to read off...:D
 
Is the question what is known as absolute value inequalities?
 

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