Question

How do you solve `\frac { 5x + 1} { x - 2} \leq 0`?

Answer 1

`x in [-1/5,2)`

Explanation:

Given
`color(white)("XXX")(5x+1)/(x-2) <= 0`

Consider the two cases (note this undefined for `x=2`):
#{: (x > 2,,x < 2), (rarr (x-2) > 0,color(white)("xxxxxxxx"),rarr (x-2) < 0), (rarr 5x+1 <= 0,,rarr 5x+1 >= 0), (rarr x <= -1/5,,rarr x >= -1/5), ("inconsistent",, rarr x in [-1/5,2)) :}#

Here is a graph of `(5x+1)/(x-2)` to help clarify:

Answer 2

.