(a) x-10<12, -3x>9 (assuming n should have been x).
x<22, -x>3, 0>3+x, -3>x, x<-3. To satisfy both inequalities, x<-3 because -3<22.
(b) 3x+1<4 OR 2x-5>7 (either one or the other, not both).
3x<3, x<1 OR 2x>12, x>6. These two inequalities are mutually exclusive so x<1 or x>6 is the solution. It implies that x cannot lie between 1 and 6 inclusively.