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anonymous
 one year ago
how do you solve
(2x^27x+3)/(6x^2+x2)<0
anonymous
 one year ago
how do you solve (2x^27x+3)/(6x^2+x2)<0

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Hero
 one year ago
Best ResponseYou've already chosen the best response.3First factor \(2x^2  7x + 3\) and \(6x^2 + x  2\)

Hero
 one year ago
Best ResponseYou've already chosen the best response.3First factor each trinomial. Let me know what you get for each.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[(2x1)(x3)/(3x+2)(2x1)\]

Hero
 one year ago
Best ResponseYou've already chosen the best response.3Next let 1/2, 3, and 3/2 be your critical points.

Hero
 one year ago
Best ResponseYou've already chosen the best response.3Create a number line with those critical points on it. dw:1438828606993:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok i understand all of that but how am i supposed to answer this?

Hero
 one year ago
Best ResponseYou've already chosen the best response.3Now you have to find the proper intervals that make \[\dfrac{(2x  1)(x  3)}{(2x  1)(3x + 2)} < 0\] true

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sot th only answer is 3/2 ?

Hero
 one year ago
Best ResponseYou've already chosen the best response.3We haven't gotten to "answers" yet. Hold down ctrl and press the minus key to zoom out.

Hero
 one year ago
Best ResponseYou've already chosen the best response.3If you zoom out, you'll see that I created a number line with 3/2, 0, 1/2, and 3 on it.

Hero
 one year ago
Best ResponseYou've already chosen the best response.3So, basically, the next step is to pick a number between any of those critical points and "test" it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so btwn 3/2 and 0, i just plug in 1?

Hero
 one year ago
Best ResponseYou've already chosen the best response.3To see if the expression on the left of the inequality is less than zero.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok if i plug 1 in it positive

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok if i plug 1 in it positive

Hero
 one year ago
Best ResponseYou've already chosen the best response.3You should start with x = 0. Zero is not a critical point so you can test it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i geta negative number

Hero
 one year ago
Best ResponseYou've already chosen the best response.3And that negative number is obviously less than zero, which means the interval (3/2, 1/2) is one of the solutions.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so do i write the answer like 3/2<x<1/2

Hero
 one year ago
Best ResponseYou've already chosen the best response.3Now understand that the solution will never include two intervals back to back so, try any number greater than 3 to check if 3 < x < ∞ is the other interval.

Hero
 one year ago
Best ResponseYou've already chosen the best response.3Which number did you test?

Hero
 one year ago
Best ResponseYou've already chosen the best response.3Test the number 2 and see what you get.

Hero
 one year ago
Best ResponseYou've already chosen the best response.3Basically, testing 2 confirms that 1/2 is not a critical point because 2x  1 is a factor of one.

Hero
 one year ago
Best ResponseYou've already chosen the best response.3So the proper solution interval is actually 3/2 < x < 3

Hero
 one year ago
Best ResponseYou've already chosen the best response.3If you have factors of one in your factorizations, just cancel them out and don't include factors of one in your testing sequence. What I mean by that is, we had \[\dfrac{(2x  1)(x  3)}{(2x  1)(3x + 2)} < 0\] And we should simplify that properly by cancelling out 2x  1 to get \[\dfrac{x  3}{3x + 2} < 0\]

Hero
 one year ago
Best ResponseYou've already chosen the best response.3So that's the expression we should have used to test the intervals. And we would only need to use 3/2 and 3 as our critical points.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok i get it! so my final answer would be 3/2<x<3 because btwn those numbers, the equation is less than 0

Hero
 one year ago
Best ResponseYou've already chosen the best response.3The simplified expression (x  3)/(3x + 2) for the given inequality is less than zero on the interval 3/2 < x < 3. There are no equations here.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok ! thanks so much for explaining all of this to me!!!!! you rock!
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