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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