Which expression is equivalent to the expression shown below? -1/2(-3/2x + 6x + 1) -3x a)3/2x - 1/2 b)6 3/4x - 1/2 c)-3/4x + 1/2 d)-5 1/4x - 1/2

The correct answer is:  [D]: " (-5 )x − " .
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Explanation:
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 " -1/2(-3/2x + 6x + 1) − 3x " ;

=  (-1/2 * -3/2 x) + (-1/2 * 6x) + (-1/2 * 1) − 3x ; 

=   [ (-1 *-3) /(2*2)] x + (-3x) + (-1/2) ] − 3x ; 

=   [ (3/4)x − 3x − (1/2) ] − 3x ; 

=   (3/4)x − 3x − (1/2) − 3x ; 

= ?? ;   →  Combine the "like terms" ; 

           → "(3/4)x − 3x − 3x " =   ?? ;

                         → "(3/4)x − 3x = "(-9/4)x";

                         → "(-9/4)x − 3x = "(-21/4)x "  =  " (-5 )x " ;  

 →  The answer is:  " (-5 )x −  " ;  
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 →   which is:
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 →   Answer choice:  [D]:  " (-5 )x −  " .
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Hope i can you!