If these 2 equations are equivalent:x > 2y+1 and (x-1)/2 <

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Discussion Overview

The discussion revolves around the equivalence of two inequalities: x > 2y + 1 and (x - 1)/2 < y. Participants explore the implications of these inequalities and seek to determine the equivalent form for the inequality x ≥ 2y + 1.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants assert that x > 2y + 1 is equivalent to (x - 1)/2 > y, suggesting a relationship between the two forms.
  • Others propose that the equivalent for x ≥ 2y + 1 should be (x - 1)/2 ≥ y, indicating a similar transformation for the non-strict inequality.
  • A participant points out that the terms used in the discussion are not "equations" but rather "inequations" or "inequalities," prompting a clarification on terminology.

Areas of Agreement / Disagreement

There is disagreement among participants regarding the equivalence of the initial inequalities and the correct terminology to use. Multiple competing views remain on how to express the equivalent forms of the inequalities.

Contextual Notes

Participants have not reached a consensus on the equivalences, and there are unresolved aspects regarding the definitions and transformations of the inequalities discussed.

xeon123
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If these 2 equations are equivalent:

x > 2y+1 and (x-1)/2 < y,

what is the equivalent equation for:

x \geq 2y+1 ?
 
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I think your first 2 equivalencies are wrong... x > 2y+1 should be equal to (x-1)/2 > y

and I believe there should be a similar result for your second equation
 


xeon123 said:
If these 2 equations are equivalent:

x > 2y+1 and (x-1)/2 < y,

what is the equivalent equation for:

x \geq 2y+1 ?
(x-1)/2\geqy
 


xeon123 and repliers,

those are not "equations."

Please use the correct term(s).

They are inequations or inequalities.
 

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