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

#### mathdaughter

##### New member
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
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
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.