# How do I solve the rational inequality (x-4)/(x+5)<4 using a TI-84?

Nov 23, 2017

See below.

#### Explanation:

There are no ways to solve a rational inequality on a TI-84 algebraically. However, graphing can give you a solution.

We will need to graph the two following equations on your TI-84 calculator:

${y}_{1} = \frac{x - 4}{x + 5}$

${y}_{2} = 4$

For reference, you basically graph the left and right sides of the original rational inequality as two separate equations. Then, you adjust the window on your TI-84 so that you can see all of the graph. Now, look for the areas where the graph of ${y}_{2}$ has a greater $y$-value than the graph of ${y}_{1}$. These area(s) will be your solution(s) to this rational inequality.

I hope that helps!