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.

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