Question

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

sqrt 28(x-1) / sqrt 8x^2

Answer 1

assuming your expression is this one:
`(√(28(x-1)))/(√(8x^2))`
we won't simplify even though we can

we can't take the square root of negative numbers nor can we divide by 0

so solve for the values that do that

ok, so the square root bits

we got √(28(x-1))
28(x-1)
this can't equal a negative
so when will it be negative?
28(x-1)<0
x-1<0
x<1
at x<1
so values less than 1 are restricted

other square root
√(8x²)
8x²<0
false


ok, and no dividing by 0

set √(8x²)=0
that is at x=0


so our restricted values are x<1 and x=0
so basically x<1 is all restricted values
so x≥1 is the set of all values that make it defined