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)#