Respuesta :
The additional operation which needed to make the expression equivalent to given expression is [tex]-\dfrac{3}{4} x[/tex]. Thus the option 3 is the correct option.
What is equivalent expression?
Equivalent expression are the expression whose result is equal to the original expression, but the way of representation is different.
Given information-
The equation given in the problem is,
[tex]\dfrac{5}{4} x+6[/tex]
Let the equation is equation number 1.
This expression is to convert in the expression, which is,
[tex]\dfrac{1}{2}x+6[/tex]
Let the above equation is equation number 2.
Let the additional operation which needed to make the expression equivalent to given expression is [tex]f(x)[/tex].
As the addition of [tex]f(x)[/tex] and equation 1 is equal to the equation 2. Therefore,
[tex]f(x)+\dfrac{5}{4} x+6=\dfrac{1}{2}x+6[/tex]
Solve the equation as,
[tex]f(x)=\dfrac{1}{2}x+6-\dfrac{5}{4} x-6\\f(x)=\dfrac{1}{2}x-\dfrac{5}{4} x\\f(x)=\dfrac{2-5}{4} x\\f(x)=\dfrac{-3}{4} x[/tex]
Hence, the additional operation which needed to make the expression equivalent to given expression is [tex]-\dfrac{3}{4} x[/tex]. Thus the option 3 is the correct option.
Learn more about the equivalent expression here;
https://brainly.com/question/2972832