Notice that all given answers options are in fraction form therefore we have to convert 0.5x into fraction form.
and in given options fraction bar '___' is use as '/' or ÷ actually '___', '/' and '÷' has same meaning divide.

1
We know that 0.5 or .5 is --- = 1/2
2
5 1
or 0.5 = --- = --- = 1/2 (in words one half)
10 2
Therefore
1
0.5x = - x or
2
x
= --- or
2
= x/2 or
= (1/2)x or
= x (1/2)

Actually 1/2x or 1/(2x) or (2x)^-1 or 1 ÷ 2x
1
means ----- which is not equal to 0.5x or x/2 or 1/2 * x
2x

we should also notice that here x is as nominator in 0.5x and from given option x is as nominator only in 2nd and 3rd option x(1/2), 1/2*x.

(x is N O M I N A T P O R )
/ | \
/ | \
/ | \
/ | \
0.5 x x(1/2) 1/2*x

but x is at denominator in given four option 1/2x, 1/(2x), (2x)^(-1)

(x is D E N O M I N A T O R )
/ | \
/ | \
/ | \
/ | \
1/2x 1/(2x) (2x)^(-1)

Therefore correct answer from given option is x (1/2) and 1/2 * x.