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Re: Which of the following represents the complete range of x [#permalink]
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17 Jun 2016, 23:44
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Found the method to solve inequalities at inequalitiestrick91482.html very useful. Applying it to the questinon above x^3  4x^5 <0 x^3(1  4x^2) <0 x3(1−2x)(1+2x)<0 This gives 3 roots  0 (by equating x3=0), x=1/2 (by equating 12x=0) and x=1/2 (by equating 1+2x=0) On a number line, we have 4 regions  1/2  0  1/2  I used 1, 1/3, 1/3 and 1 as data sets for each region and put them in x3(1−2x)(1+2x) eq. For x=1, x3(1−2x)(1+2x) is a +ve expression (1*3*1=3). So function is +vw for x< 1/2  range1 For x=1/3, x3(1−2x)(1+2x) is a ve expression (1/27*5/3*1/3). So fn is ve for 1/2<=x<0  range 2 For x=1/3, x3(1−2x)(1+2x) is +ve. So fn is +ve for 0<=x<1/2 range 3 For x=1, x3(1−2x)(1+2x) is ve. So fn is ve for 1/2<=x range 4 The original expression (condition) is x^3  4x^5 <0. So we are interested in ve function only which are given by ranges 2 and 4 only. Thus answer is 1/2<=x<0 and 1/2<=x which is same as choice C (–½ < x < 0 or ½ < x)



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Re: Which of the following represents the complete range of x [#permalink]
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09 Jul 2016, 22:37
In this case we have points 1/2 ,0, 1/2 So the sequence of signs should be ++ So the range should be x<1/2 or 0<x<1/2 But the OA is different. where did i go wrong ?



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Re: Which of the following represents the complete range of x [#permalink]
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11 Jul 2016, 22:10
Anjalika123 wrote: In this case we have points 1/2 ,0, 1/2 So the sequence of signs should be ++ So the range should be x<1/2 or 0<x<1/2 But the OA is different. where did i go wrong ? Recall that if you are going to start with a positive sign from the rightmost region, the factors should be in the form (x  a) etc (a  x) changes the entire thing. x^3(1−2x)(1+2x)<0 has ( 1 2x) which is 2*(1/2  x). This is of the form (a  x). You need to multiply the inequality by 1 here to get x^3 * (2x  1) * (1 + 2x) > 0 Now you will get the correct answer.
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Re: Which of the following represents the complete range of x [#permalink]
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25 Jul 2016, 19:13
x^3 – 4x^5 < 0 x^3 < 4x^5 x * x * x < 4 * x * x * x * x * x Cancelling both sides... 1 < 4 * x * x 1/4 < x^2 sqrt(1/4) < x... so, –½ < x or ½ < x. there is a tricky situation here where x should be more than –½, but x should also be more than ½. But we know 0 cannot be an option, as 0  0 is not < 0. Hence, option C..



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Re: Which of the following represents the complete range of x [#permalink]
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08 Oct 2016, 05:13
Bunuel wrote: 144144 wrote: Thanks Bunuel. +1
A question  what is the best way u use to know if the "good" area is above or below?
i mean  what was the best way for u to know that its between 1/2 to 0
i used numbers ex. 1/4 but it consumes time! is there any better technique?
thanks. Check the link in my previous post. There are beautiful explanations by gurpreetsingh and Karishma. General idea is as follows: We have: \((1+2x)*x^3*(12x)<0\) > roots are 1/2, 0, and 1/2 (equate the expressions to zero to get the roots and list them in ascending order), this gives us 4 ranges: \(x<\frac{1}{2}\), \(\frac{1}{2}<x<0\), \(0<x<\frac{1}{2}\) and \(x>\frac{1}{2}\) > now, test some extreme value: for example if \(x\) is very large number than first two terms ((1+2x) and x) will be positive but the third term will be negative which gives the negative product, so when \(x>\frac{1}{2}\) the expression is negative. Now the trick: as in the 4th range expression is negative then in 3rd it'll be positive, in 2nd it'l be negative again and finally in 1st it'll be positive: +  + . So, the ranges when the expression is negative are: \(\frac{1}{2}<x<0\) (2nd range) or \(x>\frac{1}{2}\) (4th range). Hope its clear. when should we include zero in the range ....please help me understand because here : inequalitiestrick91482.html @fluke's solution doesnt contain 0 in the set of ranges. :/ HELP



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Re: Which of the following represents the complete range of x [#permalink]
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08 Oct 2016, 05:50
nishantdoshi wrote: Bunuel wrote: 144144 wrote: Thanks Bunuel. +1
A question  what is the best way u use to know if the "good" area is above or below?
i mean  what was the best way for u to know that its between 1/2 to 0
i used numbers ex. 1/4 but it consumes time! is there any better technique?
thanks. Check the link in my previous post. There are beautiful explanations by gurpreetsingh and Karishma. General idea is as follows: We have: \((1+2x)*x^3*(12x)<0\) > roots are 1/2, 0, and 1/2 (equate the expressions to zero to get the roots and list them in ascending order), this gives us 4 ranges: \(x<\frac{1}{2}\), \(\frac{1}{2}<x<0\), \(0<x<\frac{1}{2}\) and \(x>\frac{1}{2}\) > now, test some extreme value: for example if \(x\) is very large number than first two terms ((1+2x) and x) will be positive but the third term will be negative which gives the negative product, so when \(x>\frac{1}{2}\) the expression is negative. Now the trick: as in the 4th range expression is negative then in 3rd it'll be positive, in 2nd it'l be negative again and finally in 1st it'll be positive: +  + . So, the ranges when the expression is negative are: \(\frac{1}{2}<x<0\) (2nd range) or \(x>\frac{1}{2}\) (4th range). Hope its clear. when should we include zero in the range ....please help me understand because here : inequalitiestrick91482.html @fluke's solution doesnt contain 0 in the set of ranges. :/ HELP We should include 0 in the range when the equation is of the form x^3  4x^5 =< 0. Notice the sign of the inequality. We have less than and equal to.
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Re: Which of the following represents the complete range of x [#permalink]
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08 Oct 2016, 05:59
and here in this partivular question we take 0 in the range because we get 0 as one of the roots...right?



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Re: Which of the following represents the complete range of x [#permalink]
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08 Oct 2016, 06:06
nishantdoshi wrote: and here in this partivular question we take 0 in the range because we get 0 as one of the roots...right? −1/2 <x<0 doesn't mean 0 is in the range. It means x could be anything less than 0 but greater than 1/2. Had the solution been −1/2 =<x=<0, we would have said 0 is in the range.
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Re: Which of the following represents the complete range of x [#permalink]
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07 Aug 2017, 14:23
we transform the inequality to x^3 ( 12x)(1+2x)<0 roots and key points are ½, 0 and ½ So 4 zones on the line starting from negative as there is a negative x in one of the inequality terms +  +  (½)0(½)> So our range is: ½<x<0 and x>½




Re: Which of the following represents the complete range of x
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