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

$x \setminus \in \left(- \setminus \infty , \frac{2}{3}\right) \setminus \cup \left[2 , \setminus \infty\right)$

#### Explanation:

Given inequality

$\frac{x + 10}{3 x - 2} \setminus \le 3$

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

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

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

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

$3 x - 2 = 0 \setminus \implies x = \frac{2}{3}$

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

$x \setminus \in \left(- \setminus \infty , \frac{2}{3}\right) \setminus \cup \left[2 , \setminus \infty\right)$