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

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Answer 1 · 2017-07-20T13:28:48

$-1/2 lt x lt -1/3$

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

enter image source here

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

$(x+2)/(2x+1) = 5$
$:. (x+2)/(2x+1) - 5 = 0$
$:. ((x+2) - 5(2x+1))/(2x+1) = 0$
$:. (x+2 - 10x-5)/(2x+1) = 0$
$:. (3x+1)/(2x+1) = 0$

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

$3x+1 => x=-1/3$
$2x+1 = 0 => x=-1/2$

Then using a graphic calculator:
enter image source here
We conclude the same result as above.

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