Question

Question 9 of 41 Which of the following inequalities represents all values of x for which the quotient below is defined? 24(x-1) = 1/8x² -) O A. x21 O B. x51 O C. X2-1 O D. xs-1

Answer 1

Given the expression:

`\sqrt[]{24(x-1)}/\sqrt[]{8x^2}`

Let's determine the inequality which represents all values of x where the quotient is defined.

Here, we are to find the domain.

Set the values in the radicand greater or equal to zero and solve for x.

We have:

`\begin{gathered} 24(x-1)\ge0 \\ \\ \text{Apply distributive property:} \\ 24x-24\ge0 \\ \\ 24x\ge24 \\ \\ \text{Divide both sides by 24:} \\ (24x)/(24)\ge(24)/(24) \\ \\ x\ge1 \end{gathered}`

Set the denominator equal to zero and solve.

`\begin{gathered} 8x^2=0 \\ \\ x^2=(0)/(8) \\ \\ x=0 \end{gathered}`

Here, the value of x should not be zero so the denominator will not tend to zero.

Therefore, we have:

x ≥ 1

This means the values of x where the expression is defined must be greater than or equal to 1.

ANSWER:

A. x ≥ 1