Question

Which expression is equivalent to

2
3
(3x + 9y) +
1
2
(4x - 2y)?
A) x + 4y
Eliminate
B) 8x - y
C) 4x + 5y
D) 2x + 5y

Answer 1

C) 4x + 5y

Explanation:

`(2)/(3)(3x+9y)+(1)/(2)(4x-2y)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=\left((2)/(3\!\!\!\!\diagup_1)\right)(3\!\!\!\!\diagup^1x})+\left((2)/(3\!\!\!\!\diagup_1)\right)(9\!\!\!\!\diagup^3y})+\left((1)/(2\!\!\!\!\diagup_1)\right)(4\!\!\!\!\diagup^2x})+\left((1)/(2\!\!\!\!\diagup_1)\right)(-2\!\!\!\!\diagup^1y})\\\\=2x+(2)(3y)+2x-y=2x+6y+2x-y\qquad\text{combine like terms}\\\\=(2x+2x)+(6y-y)=4x+5y`