How do I solve the rational inequality $(x+10)/(3x-2)<=3$ using a TI-84?

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Answer 1 · 2018-07-28T18:23:11

$x\in(-\infty, 2/3)\cup[2, \infty)$

Given inequality

${x+10}/{3x-2}\le 3$

${x+10}/{3x-2}-3\le 0$

$\frac{-8(x-2)}{3x-2}\le 0$

$\frac{x-2}{3x-2}\ge 0$

Setting $x-2=0\implies x=2$ &

$3x-2=0\implies x=2/3$

Specifying the critical points on the number line & dividing in the positive & negative intervals. It gives the solution

$x\in(-\infty, 2/3)\cup[2, \infty)$

How do I solve the rational inequality (x+10)/(3x-2)<=3(x+10)/(3x-2)<=3 using a TI-84?