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Which of the following inequalities is equal to x3x<8? [#permalink]
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25 Aug 2017, 01:17
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Which of the following inequalities is equal to x3x<8? A. 0<x<4 B. 0<x<2 C. 2<x<4 D. 2<x<2 E. 2<x<0
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Re: Which of the following inequalities is equal to x3x<8? [#permalink]
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25 Aug 2017, 01:44
MathRevolution wrote: Which of the following inequalities is equal to x3x<8?
A. 0<x<4 B. 0<x<2 C. 2<x<4 D. 2<x<2 E. 2<x<0 I believe there is a TYPO in Q and Q means x3*x<8 best way is working on the choices substiute x as 0..\(030<8....0<8\).. True so choice A and B, which exclude 0 can be eliminatedNow substitute x as 3\(333=0<8\)... true eliminate B and D as they exclude 3ans C
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Re: Which of the following inequalities is equal to x3x<8? [#permalink]
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25 Aug 2017, 01:52



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Re: Which of the following inequalities is equal to x3x<8? [#permalink]
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25 Aug 2017, 03:11
Bunuel can show the process that how can we get the range of x in an absolute inequality ?



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Which of the following inequalities is equal to x3x<8? [#permalink]
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Updated on: 25 Aug 2017, 03:38
MathRevolution wrote: Which of the following inequalities is equal to x3x<8?
A. 0<x<4 B. 0<x<2 C. 2<x<4 D. 2<x<2 E. 2<x<0 Case 1: if \(x >0\) then \(x = x\), hence the equation can be written as \(x3x<8\), or \(2x<8\) or \(2x<8\) therefore \(x<4\)(1) Case 2: if \(x<0\), then \(x = x\), hence the equation can be written as \(x 3(x)<8\), or \(x+3x<8\), or \(4x<8\) or \(x<2\) therefore \(x<2\) or \(x>2\)(2) Case 3: if \(x = 0\), then it will always satisfy the inequality combining cases 1, 2 & 3 we get \(2<x<4\) Option \(C\)
Originally posted by niks18 on 25 Aug 2017, 03:32.
Last edited by niks18 on 25 Aug 2017, 03:38, edited 1 time in total.



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Re: Which of the following inequalities is equal to x3x<8? [#permalink]
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25 Aug 2017, 03:34
MathRevolution wrote: Which of the following inequalities is equal to x3x<8?
A. 0<x<4 B. 0<x<2 C. 2<x<4 D. 2<x<2 E. 2<x<0 \(x3x<8 \iff 8 < x3x < 8\) Case 1: \(x \geq 0\) We have \(8 < x  3x < 8 \implies 8 < 2x < 8 \implies 4 > x > 4\) Thus \(0 \leq x < 4\) Case 2: \(x < 0\) We have \(8 < x + 3x < 8 \implies 8 < 4x < 8 \implies 2 < x < 2\) Thus \(2 < x < 0\) Combine both 2 cases, we have \(2 < x < 4\). Answer C
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Which of the following inequalities is equal to x3x<8? [#permalink]
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25 Aug 2017, 10:34
MathRevolution wrote: Which of the following inequalities is equal to x3x<8?
A. 0<x<4 B. 0<x<2 C. 2<x<4 D. 2<x<2 E. 2<x<0 Answered this question using plugin method. Plug 1 and 3, if both of the numbers satisfy the equation, then we can choose C. Absolute in absolute makes me confused
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Re: Which of the following inequalities is equal to x3x<8? [#permalink]
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25 Aug 2017, 10:39
niks18 wrote: MathRevolution wrote: Which of the following inequalities is equal to x3x<8?
A. 0<x<4 B. 0<x<2 C. 2<x<4 D. 2<x<2 E. 2<x<0 Case 1: if \(x >0\) then \(x = x\), hence the equation can be written as \(x3x<8\), or \(2x<8\) or \(2x<8\) therefore \(x<4\)(1) Case 2: if \(x<0\), then \(x = x\), hence the equation can be written as \(x 3(x)<8\), or \(x+3x<8\), or \(4x<8\) or \(x<2\) therefore \(x<2\) or \(x>2\)(2) Case 3: if \(x = 0\), then it will always satisfy the inequality combining cases 1, 2 & 3 we get \(2<x<4\) Option \(C\) Dear niks18 , can you please explain more the one that I highlighted?
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Re: Which of the following inequalities is equal to x3x<8? [#permalink]
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25 Aug 2017, 10:49
septwibowo wrote: niks18 wrote: MathRevolution wrote: Which of the following inequalities is equal to x3x<8?
A. 0<x<4 B. 0<x<2 C. 2<x<4 D. 2<x<2 E. 2<x<0 Case 1: if \(x >0\) then \(x = x\), hence the equation can be written as \(x3x<8\), or \(2x<8\) or \(2x<8\) therefore \(x<4\)(1) Case 2: if \(x<0\), then \(x = x\), hence the equation can be written as \(x 3(x)<8\), or \(x+3x<8\), or \(4x<8\) or \(x<2\) therefore \(x<2\) or \(x>2\)(2) Case 3: if \(x = 0\), then it will always satisfy the inequality combining cases 1, 2 & 3 we get \(2<x<4\) Option \(C\) Dear niks18 , can you please explain more the one that I highlighted? Hi septwibowoits a property of mod function which can be explained as follows  let \(x = 3\), then \(3 = 3\) this is same as \((3)\) hence if \(x<0\) (i.e negative), then \(x = x\)



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Re: Which of the following inequalities is equal to x3x<8? [#permalink]
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25 Aug 2017, 10:57
niks18 wrote: Hi septwibowoits a property of mod function which can be explained as follows  let \(x = 3\), then \(3 = 3\) this is same as \((3)\) hence if \(x<0\) (i.e negative), then \(x = x\) Ah!! thanks niks18 , at first I thought that how can an absolute results a negative number. Now I got it, (X) is not negative because X itself is negative. Many thanks!
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Re: Which of the following inequalities is equal to x3x<8? [#permalink]
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27 Aug 2017, 19:11
=> 8 < x3x <8 1) x >= 0 8 < x3x < 8 8 < 2x < 8 4 < x < 4 0 <= x < 4 2) x < 0 8 < x3x < 8 8 < x+3x < 8 8 < 4x < 8 2 < x < 2 2 < x < 0 Thus, 2 < x < 4
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Re: Which of the following inequalities is equal to x3x<8? [#permalink]
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12 Sep 2017, 11:48
niks18 wrote: MathRevolution wrote: Which of the following inequalities is equal to x3x<8?
A. 0<x<4 B. 0<x<2 C. 2<x<4 D. 2<x<2 E. 2<x<0 Case 1: if \(x >0\) then \(x = x\), hence the equation can be written as \(x3x<8\), or \(2x<8\) or \(2x<8\) therefore \(x<4\)(1) Case 2: if \(x<0\), then \(x = x\), hence the equation can be written as \(x 3(x)<8\), or \(x+3x<8\), or \(4x<8\) or \(x<2\) therefore \(x<2\) or \(x>2\)(2) Case 3: if \(x = 0\), then it will always satisfy the inequality combining cases 1, 2 & 3 we get \(2<x<4\) Option \(C\) Hey Have I interpreted it correctly? 1) If x>=0 x= x 2) If x<0 x=x because ((x)) 3) If x<0 and the sign is also given, then x=x



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Which of the following inequalities is equal to x3x<8? [#permalink]
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12 Sep 2017, 12:24
Shiv2016 wrote: niks18 wrote: MathRevolution wrote: Which of the following inequalities is equal to x3x<8?
A. 0<x<4 B. 0<x<2 C. 2<x<4 D. 2<x<2 E. 2<x<0 Case 1: if \(x >0\) then \(x = x\), hence the equation can be written as \(x3x<8\), or \(2x<8\) or \(2x<8\) therefore \(x<4\)(1) Case 2: if \(x<0\), then \(x = x\), hence the equation can be written as \(x 3(x)<8\), or \(x+3x<8\), or \(4x<8\) or \(x<2\) therefore \(x<2\) or \(x>2\)(2) Case 3: if \(x = 0\), then it will always satisfy the inequality combining cases 1, 2 & 3 we get \(2<x<4\) Option \(C\) Hey Have I interpreted it correctly? 1) If x>=0 x= x 2) If x<0 x=x because ((x)) 3) If x<0 and the sign is also given, then
x=xHi Shiv2016The highlighted part is not correct. As you have already mentioned that \(x<0\) i.e \(x\) is negative and we know that mod function is always positive so as per your equation \(LHS=RHS\) implies that \(positive = negative\) which is incorrect. assume that x = 2 so per statement 3: (2) = 2, or 2=2 Not possible Also you have added one extra "" in statement 2



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Re: Which of the following inequalities is equal to x3x<8? [#permalink]
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12 Sep 2017, 12:38
So does that mean we have to always take x= x when x<0 for the simple reason that  always gives positive value? I am actually confused because it took me some time to understand absolute values and I started solving questions this way only. I always took  as positive but in some questions,  gives negative value e.g. if x<0, then x= x which is said to be positive in some solutions.
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Re: Which of the following inequalities is equal to x3x<8? [#permalink]
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12 Sep 2017, 12:49
Shiv2016 wrote: So does that mean we have to always take x= x when x<0 for the simple reason that  always gives positive value?
I am actually confused because it took me some time to understand absolute values and I started solving questions this way only. I always took  as positive but in some questions,  gives negative value e.g. if x<0, then x= x which is said to be positive in some solutions. Hi Shiv20161. Mod is always positive 2. Negative sign inside mod function can be converted to positive i.e. \(x\) is same as \(x\) 3. In an Equality \(LHS = RHS\) when we are saying that \(x<0\), then \(x\) cannot be equal to \(x\) but we can say that \(x=x\) assume \(x=2; (2)=(2)\), or \(2=2\), which is perfectly fine Hence whenever \(x<0\), we can write mod function as \(x=x\) for \(x>0; x=x\)




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