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

2 Answers
Sep 12, 2017

#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:
enter image source here

Sep 12, 2017

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