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

mathdaughter

New member
Joined
Sep 6, 2017
Messages
18
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,
 

ksdhart2

Full Member
Joined
Mar 25, 2016
Messages
964
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?
 

mathdaughter

New member
Joined
Sep 6, 2017
Messages
18
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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