solve 2sinx+√3<0 for 0<x<2π

Answer 1

sinx < -√3/2

consider sinx = -√3/2
by the CAST rule and knowing that sin 30° = +√3/2
x = 210° or x = 330°

also, you should know the general shape of the sine curve.
from the above the curve would be below -√3/2 between 210° and 330°
or in radians:
7π/6 < x < 11π/6

verification:
http://www.wolframalpha.com/input/?i=sinx++%3C+-%E2%88%9A3%2F2+from+0+to+2%CF%80