Question

In order to make the expression below equivalent to 1 2 x 6, which additional operation should be included in the expression? Use the drop-down menu to select the operation. Five-fourths x 6.

Answer 1

The additional operation which needed to make the expression equivalent to given expression is $-\dfrac{3}{4} x$. 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,

$\dfrac{5}{4} x+6$

Let the equation is equation number 1.

This expression is to convert in the expression, which is,

$\dfrac{1}{2}x+6$

Let the above equation is equation number 2.

Let the additional operation which needed to make the expression equivalent to given expression is $f(x)$.

As the addition of $f(x)$ and equation 1 is equal to the equation 2. Therefore,

$f(x)+\dfrac{5}{4} x+6=\dfrac{1}{2}x+6$

Solve the equation as,

$f(x)=\dfrac{1}{2}x+6-\dfrac{5}{4} x-6\\f(x)=\dfrac{1}{2}x-\dfrac{5}{4} x\\f(x)=\dfrac{2-5}{4} x\\f(x)=\dfrac{-3}{4} x$

Hence, the additional operation which needed to make the expression equivalent to given expression is $-\dfrac{3}{4} x$. Thus the option 3 is the correct option.

Learn more about the equivalent expression here;

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