Question

How do you solve `\frac{x + 2}{x - 5} \leq 1`?

Answer 1

`x < 5`

Explanation:

Given
`color(white)("XXX")(x+2)/(x-5) <=1`

If
#{:((x-5)" is positive",color(white)("XXX"),(x-5)" is zero",color(white)("xxx"),(x-5)"is negative"), (x+2 <=x-5,,"undefined",,x+2 >= x-5), (2 <= -5,,,,2>=-5), ("never true",,,,"always true") :}#

Therefore `(x-5)` is neagative
`color(white)("XXXXXXXXXXXXX")rarr x < 5`