1. Multiples

If 7x is a multiple of 210, must x be a multiple of 12?

Thank you!

2. Re: Multiples

Originally Posted by ChickenWings

If 7x is a multiple of 210, must x be a multiple of 12?

Thank you!
Let $x=30$

$7x=7\cdot 30 = 210$ is a multiple of $210$

$30$ is not a multiple of $12$

the strategy for solving is

$7x=210k$ for some integer $k$

$x = 30k$

choose some $k$ such that $30k$ is not a multiple of 12. $k=1$ works as shown above.

3. Re: Multiples

Thank you so much!