Question

Plz help! ASAP! What is the expression shown below

Answer 1

we are given

$\frac{1}{2} (\frac{3}{2} x+6x+1)-3x$

step-1: Simplify expression inside parenthesis

we will combine like terms

so, firstly we will take common denominator

$\frac{1}{2} (\frac{3}{2} x+\frac{2*6}{1*2}x+1)-3x$

$\frac{1}{2} (\frac{3x+12x}{2} +1)-3x$

$\frac{1}{2} (\frac{15x}{2} +1)-3x$

step-2: Distribute 1/2 inside

$=\frac{1}{2} *\frac{15x}{2} +1*\frac{1}{2}-3x$

$=\frac{15x}{4} +\frac{1}{2} -3x$

step-3: Combine like terms

$=\frac{15x}{4}+3x +\frac{1}{2}$

We can find common denominator

$=\frac{15x}{4}-\frac{4*3x}{4*1} +\frac{1}{2}$

$=\frac{15x}{4}-\frac{12x}{4} +\frac{1}{2}$

$=\frac{15x-12x}{4} +\frac{1}{2}$

$=\frac{3x}{4} +\frac{1}{2}$

we can also write it as in mixed form

$=\frac{3}{4}x +\frac{1}{2}$

so, we will get

$\frac{1}{2} (\frac{3}{2} x+6x+1)-3x=\frac{3}{4}x +\frac{1}{2}$

option-C.............Answer