How do I solve the rational inequality (3x-2)/(x+2)<=1/3 using a TI-83?

1 Answer
Rachel
Mar 8, 2016

x<=1

Explanation:

This problem can be solved multiple ways, either through graphing or algebraically. Because I don't have a TI-83 I'm going to solve this problem algebraically.

We start with (3x-2)/(x+2)<=1/3

The first thing I am going to do is get rid of the x+2 in the denominator by multiplying both sides by x+2 to give me 3x-2<=1/3x+2/3. Now I just add 2 on both sides to arrive at 3x<=1/3x+2/3+2, or 3x<=1/3x+8/3. From there I subtract 1/3x on both sides, which gives us 3x-1/3x<=8/3, which can be rewritten as 8/3x<=8/3. Divide both sides by 8/3, and we get x<=1.

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