How do I solve the rational inequality #(x^2-x-6)/(x+2)<=-3# using a TI-83?

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Answer 1 · 2014-10-19T15:39:48

If you do not have to use a calculator, then here is how.

By factoring out the numerator,

#{(x+2)(x-3)}/{x+2} le -3#

by cancelling out #(x+2)#'s,
(Note that #x ne-2# since we cannot have a zero denominator.)

#Rightarrow x-3 le -3#

by adding #3#,

#Rightarrow x le 0#

Hence, the solution set of the inequality is

#(-infty,-2)cup(-2,0]#.

I hope that this was helpful.