Solve the inequality for x, given that (4x - 16) / [(x - 3)(x - 9)] <

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SUMMARY

The inequality (4x - 16) / [(x - 3)(x - 9)] < 0 can be solved by first factoring the numerator to 4(x - 4) and analyzing the critical points where the expression equals zero or is undefined. The critical points are x = 3, x = 4, and x = 9. By testing intervals around these points, one can determine where the rational expression is negative, leading to the solution set for x.

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Homework Statement



Solve the inequality for x, given that (4x - 16) / [(x - 3)(x - 9)] < 0


Homework Equations



I can't think of any for this type of problem...


The Attempt at a Solution



(4x - 16) / [(x - 3)(x - 9)] < 0
4(x - 4) / [(x - 3)(x - 9)] < 0


I'm not sure where to go from here. I haven't worked one of these types of problems in awhile...
 
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agl89 said:

Homework Statement



Solve the inequality for x, given that (4x - 16) / [(x - 3)(x - 9)] < 0


Homework Equations



I can't think of any for this type of problem...


The Attempt at a Solution



(4x - 16) / [(x - 3)(x - 9)] < 0
4(x - 4) / [(x - 3)(x - 9)] < 0


I'm not sure where to go from here. I haven't worked one of these types of problems in awhile...

Multiply both sides of the inequality by something, to get rid of the denominator...
 
Start by looking for the x values that make each individual factor 0: what do you know about how the sign of a rational expression behaves between locations where the expression is zero or undefined?
 

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