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Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
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Updated on: 23 Aug 2018, 20:25
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Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
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Updated on: 27 Aug 2018, 01:07
Solution Given:• An inequality, \((x+1) (123x)^5 (x+3) (5x) < 0\)
To find:• The range of x, that satisfies the above inequality
Approach and Working: • So, if we observe carefully, the inequality given to us can be written as,
o \((x+1) (123x) (123x)^4 (x+3) (5x) < 0\) • We know that, any number of the form \(N^2\) is always positive, expect for N = 0.
o So, we can say that, \((123x)^4\) is always positive, expect for x = 4, o Thus, the inequality can be written as (x+1) (123x) (x+3) (5x) < 0 • Now, let’s multiply the inequality by 1, twice, to make the coefficients of x, in 123x and 5x, positive
o And, note that the inequality sign does not change as we are multiplying it by 1, twice • Thus, the inequality becomes, (x+1) (3x  12) (x+3) (x  5) < 0 • The zero points of this inequality are x = 1, x = 4, x = 3 and x = 5 • Plot these points on the number line.
o Since, 5 is the greatest among all, the inequality will be positive, for all the points to the right of 5, on the number line o And, it is negative, in the region, between 4 and 5 o It is again positive in the region, between 1 and 4 o And, it is again negative in the region, between 3 and 1 o And, it is positive for all the values of x, less than 3 Therefore, the range of x is 5 < x < 4 and 3 < x < 1 Hence, the correct answer is option D. Answer: D
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Re: Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
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23 Aug 2018, 05:08
EgmatQuantExpert wrote: Solving inequalities Number Line Method  Practice Question #2
Find the range of values of x such that \((x+1) (123x)^5 (x+3) (5x) < 0.\) A. \(x > 5\) B. \(4 < x < 5\) C. \(3 < x < 2\) D. \((3< x < 1) and (4 < x < 5)\) E. \((x < 3) and (x > 5)\)
\((x+1) (123x)^5 (x+3) (5x) < 0\) Or, \(243\left(x4\right)^5\left(x5\right)\left(x+1\right)\left(x+3\right)<0\) using wavy curve method: \(3<x<1\quad \mathrm{or}\quad \:4<x<5\) Ans. (D)
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Re: Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
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05 Sep 2018, 04:38
PKN wrote: EgmatQuantExpert wrote: Solving inequalities Number Line Method  Practice Question #2
Find the range of values of x such that \((x+1) (123x)^5 (x+3) (5x) < 0.\) A. \(x > 5\) B. \(4 < x < 5\) C. \(3 < x < 2\) D. \((3< x < 1) and (4 < x < 5)\) E. \((x < 3) and (x > 5)\)
\((x+1) (123x)^5 (x+3) (5x) < 0\) Or, \(243\left(x4\right)^5\left(x5\right)\left(x+1\right)\left(x+3\right)<0\) using wavy curve method: \(3<x<1\quad \mathrm{or}\quad \:4<x<5\) Ans. (D) Hello PKN hope you are having a good day. I attempted this question using the wavy line method as well but didn't answer correctly. To rearrange the expressions in the (xa)(xb) form and i multiplied through by 1 and this changed the inequality sign to >0 but I didn't arrive at the right answer anyway. Could you please elaborate on how you rearranged 5x to x5 without changing the sign of the inequality. Thanks. I'm not a Math guru, just pushing hard for a 700 score. Posted from my mobile device



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Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
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05 Sep 2018, 10:21
Kem12 wrote: PKN wrote: EgmatQuantExpert wrote: Solving inequalities Number Line Method  Practice Question #2
Find the range of values of x such that \((x+1) (123x)^5 (x+3) (5x) < 0.\) A. \(x > 5\) B. \(4 < x < 5\) C. \(3 < x < 2\) D. \((3< x < 1) and (4 < x < 5)\) E. \((x < 3) and (x > 5)\)
\((x+1) (123x)^5 (x+3) (5x) < 0\) Or, \(243\left(x4\right)^5\left(x5\right)\left(x+1\right)\left(x+3\right)<0\) using wavy curve method: \(3<x<1\quad \mathrm{or}\quad \:4<x<5\) Ans. (D) Hello PKN hope you are having a good day. I attempted this question using the wavy line method as well but didn't answer correctly. To rearrange the expressions in the (xa)(xb) form and i multiplied through by 1 and this changed the inequality sign to >0 but I didn't arrive at the right answer anyway. Could you please elaborate on how you rearranged 5x to x5 without changing the sign of the inequality. Thanks. I'm not a Math guru, just pushing hard for a 700 score. Posted from my mobile deviceHi Kem12, Greetings of the day!! Given f(x)<0. Notice that two of the factors of f(x) are not in the form of \((xa)^n\) rather they are in the form of \((ax)^n\). Our requirement: All factors must present in the form \((xa)^n\), If not, then we have to convert to \((ax)^n\). So, odd forms are: \((123x)^5\) & (5x) 1) \((123x)^5\) can be written as:\(((3x12))^5\) or, \((1)^5*(3x12)^5\) or, \((3)^5*(x4)^5\) Or, \(243(x4)^5\) 2) (5x) can be written as : (x5) Now f(x)= \((x+1) (123x)^5 (x+3) (5x)\)=\((x(1))*{243(x4)^5}*(x(3))*{(x5)}=243(x(1))*(x4)^5*(x(3))*(x5)\) Now simplified expression as per desired form: \(243(x(1))*(x4)^5*(x(3))*(x5)<0\) Or, \((x(1))*(x4)^5*(x(3))*(x5)<0\) Step1critical points: 1, 4,3,5 Step2Arrange the critical points in ascending fashion:3,1,4,5 Step3Draw the curve. Please revert in case of any difficulty in step3. All the best. I am no expert, I am at learning stage.
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Re: Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
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07 Sep 2018, 00:39
Hi PKN, thanks for the explanation. But I just want to confirm whether in the 3rd step, the negative in (x5) and 243(x4)^5 canceled because of even number of negatives, right? If the inequality were just (x+1) (x4) (x5) <0 how will we go about this? Thanks. Posted from my mobile device



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Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
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07 Sep 2018, 01:17
Kem12 wrote: Hi PKN, thanks for the explanation. But I just want to confirm whether in the 3rd step, the negative in (x5) and 243(x4)^5 canceled because of even number of negatives, right? If the inequality were just (x+1) (x4) (x5) <0 how will we go about this? Thanks. Posted from my mobile deviceHi Kem12, You know , multiplying negative sign an even number of times results positive polarity. 1) ()*()=(+) 2) ()*(+)=() 3) ()*()*()=() flip of sign in inequalities: 1. Whenever you multiply or divide an inequality by a positive number, you must keep the inequality sign. 2. Whenever you multiply or divide an inequality by a negative number, you must flip the inequality sign. Refer note(2) above, ' (x+1) (x4) {(x5)} <0 Or, (1)(x+1) (x4) (x5)<0 Or, (1)*(1)(x+1) (x4) (x5) >0*(1) (flip of sign occurs , multiplying both side of inequality by (1)) Or, (x+1) (x4) (x5)>0 ((1)*(1)=+1 and 0*(1)=0) Hope it helps.
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Re: Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
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07 Sep 2018, 04:07
Totally clear now. Thanks PKNPosted from my mobile device



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Re: Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5
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07 Sep 2018, 04:15
Kem12 wrote: Totally clear now. Thanks PKNPosted from my mobile deviceNeed not to mention. (blue color) depicts everything. You are always welcome.
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Re: Find the range of values of x such that [m](x+1) (123x)^5 (x+3) (5 &nbs
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