finding integers from inequality

Question

$$14 - 3x < 41$$ $$2x - 15 < -3$$ How many possible integer values exist for x?

One have done, 14 - 3x < 41 ;

-3x < 27 ;

x > 9 . (I guess he done wrong here. Am I right?)

and 2x - 15 < -3;

2x < 12 ;

x < 6

There can be no value of x that is both less than 6 and greater than 9. Therefore, there are 0 possible integer values of x in this system.

Answer 1

$-3x<27\iff 3x>-27\implies x>-9$ not $x>9$

i..e, $14-3x<41\iff 3x>14-41, 3x>-27\iff x>-9$

$2x-15<-3\iff 2x<-3+15=12\iff x<6$

$-9<x<6$

As $x$ is integer $-8\le x\le 5$

So , there will be $5-(-8)+1$(due to $0$) values