Question

Which inequality represents all values of x for which the quotient below is

defined?
28(x-1) = 8x?
O A. x less than or equal to -1
B.x great than or equal to 1
O C. x> 1
O D. x<-1

Answer 1

You can re-write this quotient this way :

`\frac{√(28(x-1))}{\sqrt{8x^(2) }} = \sqrt{ (28(x-1))/(8x^(2) ) }\\`

What's inside the square root must be greater than or equal to 0, because the domain of the square root function is defined on R+ (which is [0,+∞))

In other word we must find x so that :

`(28(x-1))/(8x^(2))\geq 0`

at the end we get

28(x-1) ≥ 0

28x - 28 ≥ 0

28x ≥ 28

x ≥ 1

So the answer is B, x ≥ 1