What is the answer to1/5z+2/3< 2

First of all, you need to find what goes into the dominators with the lcm. It would be 15. You would then multiply both the numerator and the denominator by 15. 
1/5z*15/1=15/5. Then you would divide 15 and 5, that would equal 3, so that would be 3z. Then you would multiply 2/3*15/1=30/3. Divide 30 and 3 and that equals 10. So now you have the expression 3z+10<2. You subtract 10 from both sides and that would be 3z<-8. Then the answer would be z<-8/3 and you would just leave the answer as it is instead of reducing it