if sin x =0.5 what values satisfy this equation in the range -180<=x<=180

Answer 1

You should know three things here:
1. the fact that sin 30° = 1/2 = 0.5 , (use your calculator to confirm)
2. the shape of the sine curve from -360° to 360°

https://www.mathsisfun.com/algebra/trig-sin-cos-tan-graphs.html

3. the CAST rule, which would tell you that the sine function is positive
in quadrants I and II

so x = 30° or x = 180°-30° or 150°
or x = -210° or -330° , look at the yellow graph

Answer 2

oops, forget about -210 and -330,
even though they are solutions, they are not within your given domain

so x = 30° or 150° for your domain