# Equations with No Solution

**URL:** <https://boards.straightdope.com/t/equations-with-no-solution/1019330>\
**Category:** Factual Questions\
**Tags:** science-math\
**Created:** [June 8, 2025, 3:14pm UTC](https://boards.straightdope.com/t/equations-with-no-solution/1019330 "2025-06-08T15:14:26Z")\
**Posts on this page:** 1\
**Showing post:** 59

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**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\
**Post date:** [June 10, 2025, 1:49pm UTC](https://boards.straightdope.com/t/equations-with-no-solution/1019330/59 "2025-06-10T13:49:37Z")

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> [@DPRK](#):
>
> So assuming there is a solution leads to a contradiction.

That’s the way some people are looking at it: 5x-5x=5 cannot have a solution (that is, cannot be true), because if we assume that it _is_ true, this leads to a contradiction (0 = 5).

But that’s not the way I’ve been looking at it (in my earlier posts #11 and #22). I’m just saying that 5x-5x=5 is equivalent to 0=5, and since the latter has no solution, the former also has no solution. I don’t _think_ there’s any need to invoke the LEM—is there?

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