mathematics - Number Theory class

A magician said to an audience member:

• Pick a number,


• Double it,


• Add $7$,


• Multiply it by $5$,


• Subtract the number you started with,


• Remove any non-zero digit from the answer,

and then tell me the remaining digits in any order.

The audience member said

$6$ and $8$.

And the magician announced,

The digit you removed was $3$, right?

The magician is right! Why? Justify!