Question

Which expresión is equivalent to -3x - (x-1) + 3/2 (3x + 3)?

A. 1/2x + 11/2
B. 1/2x + 7/2
C. 5/2x + 11/2
D. 5/2x + 7/2

Answer 1

`\large\boxed{A.\ (1)/(2)x+(11)/(2)}`

Explanation:

`-3x-(x-1)+(3)/(2)(3x+3)\qquad\text{use the distributive property}\\\\=-3x-x-(-1)+\left((3)/(2)\right)(3x)+\left((3)/(2)\right)(3)\\\\=-3x-x+1+(9)/(2)x+(9)/(2)\qquad\text{combine like terms}\\\\=\bigg(-3x-x+(9)/(2)x\bigg)+\bigg(1+(9)/(2)\bigg)\\\\=\bigg((-6)/(2)x-(2)/(2)x+(9)/(2)x\bigg)+\bigg((2)/(2)+(9)/(2)\bigg)\\\\=(-6-2+9)/(2)x+(2+9)/(2)=(1)/(2)x+(11)/(2)`