Question

Which expressions are equivalent? Select two answers.

Answer 1

Answer:

A, C

Step-by-step explanation:

The distributive property:

a(b + c) = ab + ac or a(b - c) = ab - ac

$A.\\\\\dfrac{1}{5}(x-50)=\dfrac{1}{5}x-\left(\dfrac{1}{5}\right)(50)=\dfrac{1}{5}x-\dfrac{50}{5}=\dfrac{1}{5}x-10\\\\B.\\\\-\dfrac{1}{3}(3x+18)=\left(-\dfrac{1}{3}\right)(3x)+\left(-\dfrac{1}{3}\right)(18)=-\dfrac{3}{3}x-\dfrac{18}{3}=-x-6\\\\-x-6\neq\dfrac{1}{3}x-6$

$C.\\\\\dfrac{1}{2}(x+16)=\dfrac{1}{2}x+\left(\dfrac{1}{2}\right)(16)=\dfrac{1}{2}x+\dfrac{16}{2}=\dfrac{1}{2}x+8\\\\D.\\\\\dfrac{1}{8}(8x+8)=\left(\dfrac{1}{8}\right)(8x)+\left(\dfrac{1}{8}\right)(8)=\dfrac{8}{8}x+\dfrac{8}{8}=x+1\\\\x+1\neq\dfrac{1}{8}x+1\\\\E.\\\\-\dfrac{1}{4}(x+2)=-\dfrac{1}{4}x+\left(\dfrac{1}{4}\right)(2)=-\dfrac{1}{4}x+\dfrac{2\!\!\!\!\diagup^1}{4\!\!\!\!\!\diagup_2}=-\dfrac{1}{4}x+\dfrac{1}{2}\\\\-\dfrac{1}{4}x+\dfrac{1}{2}\neq-\dfrac{1}{4}x+2$