Answer:OPTION A and OPTION CStep-by-step explanation:OPTION A:[tex]$ \frac{1}{5}x - 10 $[/tex] and [tex]$ \frac{1}{5}(x - 50) $[/tex]Consider [tex]$ \frac{1}{5}(x - 50) = \frac{x}{5} - \frac{50}{5} $[/tex]This is equal to [tex]$ \frac{1}{5}x - 10 $[/tex].This is exactly the first expression. So, we say both expressions are equivalent.OPTION B:[tex]$ \frac{1}{3} x - 6 $[/tex] and [tex]$ - \frac{1}{3}(3x + 18) $[/tex]Distributing [tex]$ -\frac{1}{3} $[/tex] to [tex]$ (3x + 18) $[/tex] we get:[tex]$ \frac{-x}{3} + \frac{-18}{3} $[/tex]⇒ [tex]$ -x - 6[/tex]This is not equivalent to the first expression.OPTION C: [tex]$ \frac{1}{2}x + 8 $[/tex] and [tex]$ \frac{1}{2}(x + 16) $[/tex][tex]$ \frac{1}{2}(x + 16) = \frac{x}{2} + \frac{16}{2} $[/tex][tex]$ \implies \frac{1}{2}x + 8 $[/tex]This is exactly the first expression. So, we say the expressions are equal.We apply similar techniques to OPTION D and OPTION E. Note that the expressions are not equal in both the options.