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What is solution of 0.5x ...?

___________________________________________

Answer
    x(1/2), 1/2 * x
Explanation

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.

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                 _____________________
                /      _____________  
               /     /        ____
              /     /        /  2  
             /  4  /  4  .  / 4  
            /    \/       \/
           /  --------------------
          /            3
        \/            2    
    
        
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