how to explain why ax = bx will always have at least one solution?

mathdaughter

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Sep 6, 2017
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The question is this:

Explain why an equation of the form ax = bx will always have at least one solution.


I know x can be zero. a can be the same as b. but what is the professional explanation?

Thanks,
 
Truthfully, I'm not really sure what more you want in order to consider it a "professional" solution/explanation. The problem asks you to explain why there's at least one solution, and you've done just that by examining the trivial case when x = 0. Then you even went above and beyond the call of duty to examine the non-trivial case when \(\displaystyle x \ne 0\) which results in a "family" of infinitely many solutions such that a = b. What else is there?
 
Truthfully, I'm not really sure what more you want in order to consider it a "professional" solution/explanation. The problem asks you to explain why there's at least one solution, and you've done just that by examining the trivial case when x = 0. Then you even went above and beyond the call of duty to examine the non-trivial case when \(\displaystyle x \ne 0\) which results in a "family" of infinitely many solutions such that a = b. What else is there?


Got it, thank you.
 
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