Question

Which inequality represent all values of x for which the quotient below is defined??

Answer 1

D.
`x>0`

Explanation:

We have been given a quotient
`√(6x^2)/√(4x)`. We are asked to find an inequality that represents all values of x for which the quotient below is defined.

We can rewrite our given expression as:

`√(6x^2)/√(4x)`

We know that a square root expression is defined for all values of x greater than or equal to 0. We also know that a fraction is defined when its denominator is greater than 0.

So our fraction will be defined for all values of x greater than 0.

`4x>0`

Upon dividing both sides of our inequality by 4, we will get:

`(4x)/(4)>(0)/(4)`

`x>0`

Therefore, the inequality
`x>0` represents all values of x for which the given quotient is defined and option D is the correct choice.