we are given
[tex] \frac{1}{2} (\frac{3}{2} x+6x+1)-3x [/tex]
step-1: Simplify expression inside parenthesis
we will combine like terms
so, firstly we will take common denominator
[tex] \frac{1}{2} (\frac{3}{2} x+\frac{2*6}{1*2}x+1)-3x [/tex]
[tex] \frac{1}{2} (\frac{3x+12x}{2} +1)-3x [/tex]
[tex] \frac{1}{2} (\frac{15x}{2} +1)-3x [/tex]
step-2: Distribute 1/2 inside
[tex] =\frac{1}{2} *\frac{15x}{2} +1*\frac{1}{2}-3x [/tex]
[tex] =\frac{15x}{4} +\frac{1}{2} -3x [/tex]
step-3: Combine like terms
[tex] =\frac{15x}{4}+3x +\frac{1}{2} [/tex]
We can find common denominator
[tex] =\frac{15x}{4}-\frac{4*3x}{4*1} +\frac{1}{2} [/tex]
[tex] =\frac{15x}{4}-\frac{12x}{4} +\frac{1}{2} [/tex]
[tex] =\frac{15x-12x}{4} +\frac{1}{2} [/tex]
[tex] =\frac{3x}{4} +\frac{1}{2} [/tex]
we can also write it as in mixed form
[tex] =\frac{3}{4}x +\frac{1}{2} [/tex]
so, we will get
[tex] \frac{1}{2} (\frac{3}{2} x+6x+1)-3x=\frac{3}{4}x +\frac{1}{2}[/tex]
option-C.............Answer
