# How do I solve the rational inequality (x+2)/(2x+1)>5 using a TI-84?

Jul 20, 2017

$- \frac{1}{2} < x < - \frac{1}{3}$

#### Explanation:

On a TI-nspire CAS we can evaluate algebraic expressions directly:

Otherwise we can solve the equation to get the critical points:

$\frac{x + 2}{2 x + 1} = 5$
$\therefore \frac{x + 2}{2 x + 1} - 5 = 0$
$\therefore \frac{\left(x + 2\right) - 5 \left(2 x + 1\right)}{2 x + 1} = 0$
$\therefore \frac{x + 2 - 10 x - 5}{2 x + 1} = 0$
$\therefore \frac{3 x + 1}{2 x + 1} = 0$

So the critical points (where a sign change can occur) are:

$3 x + 1 \implies x = - \frac{1}{3}$
$2 x + 1 = 0 \implies x = - \frac{1}{2}$

Then using a graphic calculator:

We conclude the same result as above.