solve 2 sin x + 1 < 0 for 0 < x < 2pi?

Answer 1

Subtract 1 from both sides:
2 sin x<-1

Divide 2 from both sides:
sin x<-1/2
x<7π/6, 11π/6

Answer 2

2sin(x) + 1 < 0
2sin(x) < -1
sin(x) < (-1/2)
x < sin^-1(-1/2)

ANS : (7/6)pi < x < (11/6)pi