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The right answer is Option A and C.Step-by-step explanation:To determine whether the expressions are equivalent or not, we will multiply the second expressions of each option and see it it is equal to first or not.A. [tex]\frac{1}{5}x-10[/tex] and [tex]\frac{1}{5}(x-10)[/tex][tex]\frac{1}{5}(x-50)\\\\\frac{1}{5}*x-50*\frac{1}{5}\\\\\frac{1}{5}x-10[/tex]The given expressions are equivalent.B. [tex]\frac{1}{3}x-6[/tex] and [tex]\frac{-1}{3}(3x+18)[/tex][tex]\frac{-1}{3}(3x+18)\\\\\frac{-1}{3}*3x+18*\frac{-1}{3}\\-x-6[/tex]The given expressions are not equivalent.C. [tex]\frac{1}{2}x+8[/tex] and [tex]\frac{1}{2}(x+16)[/tex][tex]\frac{1}{2}(x+16)\\\frac{1}{2}*x+16*\frac{1}{2}\\\frac{1}{2}x+8[/tex]The given expressions are equivalent.D. [tex]\frac{1}{8}x+1[/tex] and [tex]\frac{1}{8}(8x+8)[/tex][tex]\frac{1}{8}(8x+8)\\\frac{1}{8}*8x+8*\frac{1}{8}\\x+1[/tex]The given expressions are not equivalent.E. [tex]\frac{-1}{2}x+2[/tex] and [tex]\frac{-1}{4}(x+2)[/tex][tex]\frac{-1}{4}(x+2)\\\frac{-1}{4}*x+2*\frac{-1}{4}\\\frac{-1}{4}x-\frac{1}{2}[/tex]The given expressions are not equivalent.The right answer is Option A and C.Keywords: fractions, linear expressionsLearn more about fractions at:brainly.com/question/2115122brainly.com/question/2154850#LearnwithBrainly