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If |12x − 3| = |3x + 15|, what is the value of x?

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If |12x − 3| = |3x + 15|, what is the value of x?  [#permalink]

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New post 10 Aug 2018, 03:47
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If |12x − 3| = |3x + 15|, what is the value of x?  [#permalink]

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New post Updated on: 10 Aug 2018, 05:18
Bunuel wrote:
If |12x − 3| = |3x + 15|, what is the value of x?

(1) x > 0
(2) x is an integer


Given, |12x − 3| = |3x + 15|
Squaring both the sides,
\((12x-3)^2=(3x+15)^2\)
Or, \(144x^2-72x+9=9x^2+90x+225\)
Or, \(135x^2-162x-216=0\)
or, \(x=-\frac{4}{5}\quad \mathrm{or}\quad \:x=2\)

Another way, 12x-3=3x+15 Or, x=2
and 12x-3=-(3x+15) or, x=-\(\frac{4}{5}\)
St1:- x > 0
Only acceptable value is 2.
Sufficient.

St2:- x is an integer
Only acceptable value is 2.
Sufficient.

Ans. (D)
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Originally posted by PKN on 10 Aug 2018, 04:48.
Last edited by PKN on 10 Aug 2018, 05:18, edited 1 time in total.
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Re: If |12x − 3| = |3x + 15|, what is the value of x?  [#permalink]

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New post 10 Aug 2018, 05:14
Bunuel wrote:
If |12x − 3| = |3x + 15|, what is the value of x?

(1) x > 0
(2) x is an integer


OA:D
If |12x − 3| = |3x + 15|, what is the value of x?

Case 1 :\(x<\frac{-15}{3}\) or \(x<-5\)
\(-(12x-3)=-(3x+15)\)
\(9x=18, x = \frac{18}{9} = 2\)
Not possible as \(x<-5\) whereas \(2>-5\)

Case 2 :\(-5≤x≤\frac{3}{12}\)

\(-(12x-3)=(3x+15)\)

\(15x=-12, x = \frac{-12}{15} = -\frac{{4}}{5}\)

Case 3: \(x>\frac{3}{12}\)

\((12x-3)=(3x+15)\)
\(9x=18, x = \frac{18}{9} = 2\)

What is value of \(x\)? Given \(x=-\frac{4}{5}\) or \(x= 2\)

Statement 1 : \(x>0\)

Out of \(-\frac{4}{5},2\); Only 2 is greater than 0
So \(x=2\)
Statement 1 alone is sufficient

Statement 2 : \(x\) is an integer
Out of \(-\frac{4}{5},2\); Only 2 is integer
So \(x=2\)
Statement 2 alone is sufficient
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Re: If |12x − 3| = |3x + 15|, what is the value of x?  [#permalink]

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New post 10 Aug 2018, 05:15
Bunuel wrote:
If |12x − 3| = |3x + 15|, what is the value of x?

|12x − 3| = |3x + 15|
Case 1:
12x − 3 = 3x + 15
9x = 18
x = 2

Case 2:
12x − 3 = -3x - 15
15x = -12
x = -12/15

Therefore x = 2 or -12/15

(1) x > 0
Which means it has to be 2 and not -12/15
Sufficient

(2) x is an integer
Which means it has to be 2 and not -12/15
Sufficient

Hence, D.
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Re: If |12x − 3| = |3x + 15|, what is the value of x?  [#permalink]

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New post 19 Apr 2019, 00:17
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Bunuel wrote:
If |12x − 3| = |3x + 15|, what is the value of x?

(1) x > 0
(2) x is an integer



|x| = \sqrt{x}

|12x-3| = |3x+15|
\sqrt{12x-3}=\sqrt{3x+15}
squaring both sides
(12x-3)^2=(3x+15)^2 ---> (12x-3)^2 - (3x+15)^2 = 0
(12x-3+3x+15)(12x-3-3x-15)=0
x=-12/15 or x= 2

Statement 1: sufficient since x can only be 2
Statement 2: sufficient since x can only be 2

Answer is D
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Re: If |12x − 3| = |3x + 15|, what is the value of x?   [#permalink] 19 Apr 2019, 00:17
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