Any help is appreciated

x < 2x - 7

-x < -7

x < 7

Therefore, the smallest integer x that works is 8.

Thank you so much I love the explanation!

Thanks guest, but you have a couple of little errors

when you multiply or divide by a negative number you have to turn the sign around

so

-x        < -7

-x*-1  >  -7*-1

x > 7

So the smallest integer that works is 8    (because 8 is bigger than 7.)

Thanks melody