Question

Which expressions are equivalent? Select two answers.

Answer 1

A, C

Explanation:

The distributive property:

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

`A.\\\\(1)/(5)(x-50)=(1)/(5)x-\left((1)/(5)\right)(50)=(1)/(5)x-(50)/(5)=(1)/(5)x-10\\\\B.\\\\-(1)/(3)(3x+18)=\left(-(1)/(3)\right)(3x)+\left(-(1)/(3)\right)(18)=-(3)/(3)x-(18)/(3)=-x-6\\\\-x-6\\eq(1)/(3)x-6`

`C.\\\\(1)/(2)(x+16)=(1)/(2)x+\left((1)/(2)\right)(16)=(1)/(2)x+(16)/(2)=(1)/(2)x+8\\\\D.\\\\(1)/(8)(8x+8)=\left((1)/(8)\right)(8x)+\left((1)/(8)\right)(8)=(8)/(8)x+(8)/(8)=x+1\\\\x+1\\eq(1)/(8)x+1\\\\E.\\\\-(1)/(4)(x+2)=-(1)/(4)x+\left((1)/(4)\right)(2)=-(1)/(4)x+(2\!\!\!\!\diagup^1)/(4\!\!\!\!\!\diagup_2)=-(1)/(4)x+(1)/(2)\\\\-(1)/(4)x+(1)/(2)\\eq-(1)/(4)x+2`