Question

Which inequality represents all values of x for which the quotient below isdefined?√x+2 / √5-x/ = division

Answer 1

To find the value of x, we have to know:

- The denominator can not be zero

- The radical must be zero or greater than zero

So, let's evaluate the numerator and the denominator

a)

`x+2\ge0`

Subtracting 2 from both sides:

`\begin{gathered} x+2-2\ge0-2 \\ x\ge-2 \end{gathered}`

b)

`5-x>0`

Adding x to both sides:

`\begin{gathered} 5-x+x>0+x \\ 5>x \\ x<5 \end{gathered}`

So, x must b greater or equal to 2 and lower than 5.

Answer:

`2\leq x<5`