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solve for X plot the points on a number line (sign analysis) find the critical values.

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First I would set the equation to equal zero. Then I would find the critical values and use sign analysis to see what part of the graphs would be positive and negative.

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Make it to where the fraction equal 0 in this equation it already does this. So the next step is to find the critical values and that would be -5 and 2/3 so then the step after that you do a sign analysis and it would look like positive before the negative five and

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If the function is factored then find the critical values that make it equal zero to use for your sign analysis. The critical values would be 2/3 and -5. So for sign analysis use those critical values and pick numbers between them to find where its negative and positive. Since it has to be less then zero the goal is to find where it equals a negative.

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(-infinity,-5)U(2/3,infinity)
<+++++++ -5 --------- (2/3)++++++++>

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set one side equal to 0
find the critical values
make a sign analysis with critical values and perform sign analysis

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1) make one side equal zero
2) find critical values (zeros and asymptotes) by setting the numerator and denominator equal to zero and solving
3) perform a sign analysis using the critical values

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Since the inequality is equal to zero, we would set the numerator and denominator to zero. We would have (2/3)/-5. Then you would take these critical values to do sign analysis like so:

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(3x-2)/(x+5)<0
3x-2=0
+2     +2
3x/3=2/3
x=2/3 (critical value)
x+5=0
-5     -5
x=-5 (critical value)
3(-6)-2/-6+5
-18-2/-1
-16/-1
16 (positive)
3(0)-2/0+5
-2/5 (negative)
3(1)-2/1+5
1/6 (positive)
Solution: (-5, 2/3)