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Which of the following could be the value of x, if |12 − 4x|
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03 Apr 2020, 08:27
03 Apr 2020, 08:27
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Question Stats:
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Which of the following could be the value of x, if |12 − 4x| + 2 = 6?
A. −4
B. −2
C. 1
D. 3
E. 4
Kudos for the right answer and explanation
A. −4
B. −2
C. 1
D. 3
E. 4
Kudos for the right answer and explanation
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: Which of the following could be the value of x, if |12 − 4x|
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28 Dec 2021, 03:09
28 Dec 2021, 03:09
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Given that |12 − 4x| + 2 = 6 and we need to find which value of x out of the option choices satisfies this.
Let's understand how to solve this problem using two methods
Method 1: Substitution
Let's take each answer choice and substitute in the question and check which one satisfies the question
A. −4 Put x = -4 in |12 − 4x| + 2 = 6. We get
| 12 - 4*(-4)| + 2 = | 12 + 16| + 2 = |28| + 2 = 28 + 2 = 30 \(\neq\) 6 => NOT POSSIBLE
B. −2 Put x = -2 in |12 − 4x| + 2 = 6. We get
| 12 - 4*(-2)| + 2 = | 12 + 8| + 2 = |20| + 2 = 20 + 2 = 22 \(\neq\) 6 => NOT POSSIBLE
C. 1 Put x = 1 in |12 − 4x| + 2 = 6. We get
| 12 - 4*1| + 2 = | 12 - 4 | + 2 = |8| + 2 = 8 + 2 = 10 \(\neq\) 6 => NOT POSSIBLE
D. 3 Put x = 3 in |12 − 4x| + 2 = 6. We get
| 12 - 4*3| + 2 = | 12 - 12| + 2 = |0| + 2 = 0 + 2 = 2 \(\neq\) 6 => NOT POSSIBLE
E. 4 Put x = 4 in |12 − 4x| + 2 = 6. We get
| 12 - 4*4| + 2 = | 12 - 16| + 2 = |-4| + 2 = 4 + 2 = 6 = 6 => POSSIBLE
Method 2: Algebra
|12 − 4x| + 2 = 6
=> |12 − 4x| = 6 -2 = 4
Divide both the sides by 4 we get
\(\frac{|12-4x|}{4} = \frac{4}{4}\)
=> | 3 - x | = 1
Now, there are two ways of solving this
Method 2.1: Squaring
Square both the sides we get
\((|3-x|)^2 = 1^2\)
=> \((3-x) ^ 2 \)= 1
=> \(3^2 + x^2 - 2*3*x\) = 1
=> 9 + \(x^2\) - 6x - 1 = 0
=> \(x^2\) - 6x + 8 = 0
=> \(x^2\) - 2x - 4x + 8 =0
=> x*(x-2) -4*(x-2) = 0
=> (x-2) * (x-4) = 0
=> x = 2 or x = 4
Method 2.2: Opening Absolute Value
| 3 - x | = 1
=> 3-x = 1 or 3-x =-1
=> x = 3-1 = 2 or x = 3+1 = 4
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
Let's understand how to solve this problem using two methods
Method 1: Substitution
Let's take each answer choice and substitute in the question and check which one satisfies the question
A. −4 Put x = -4 in |12 − 4x| + 2 = 6. We get
| 12 - 4*(-4)| + 2 = | 12 + 16| + 2 = |28| + 2 = 28 + 2 = 30 \(\neq\) 6 => NOT POSSIBLE
B. −2 Put x = -2 in |12 − 4x| + 2 = 6. We get
| 12 - 4*(-2)| + 2 = | 12 + 8| + 2 = |20| + 2 = 20 + 2 = 22 \(\neq\) 6 => NOT POSSIBLE
C. 1 Put x = 1 in |12 − 4x| + 2 = 6. We get
| 12 - 4*1| + 2 = | 12 - 4 | + 2 = |8| + 2 = 8 + 2 = 10 \(\neq\) 6 => NOT POSSIBLE
D. 3 Put x = 3 in |12 − 4x| + 2 = 6. We get
| 12 - 4*3| + 2 = | 12 - 12| + 2 = |0| + 2 = 0 + 2 = 2 \(\neq\) 6 => NOT POSSIBLE
E. 4 Put x = 4 in |12 − 4x| + 2 = 6. We get
| 12 - 4*4| + 2 = | 12 - 16| + 2 = |-4| + 2 = 4 + 2 = 6 = 6 => POSSIBLE
Method 2: Algebra
|12 − 4x| + 2 = 6
=> |12 − 4x| = 6 -2 = 4
Divide both the sides by 4 we get
\(\frac{|12-4x|}{4} = \frac{4}{4}\)
=> | 3 - x | = 1
Now, there are two ways of solving this
Method 2.1: Squaring
Square both the sides we get
\((|3-x|)^2 = 1^2\)
=> \((3-x) ^ 2 \)= 1
=> \(3^2 + x^2 - 2*3*x\) = 1
=> 9 + \(x^2\) - 6x - 1 = 0
=> \(x^2\) - 6x + 8 = 0
=> \(x^2\) - 2x - 4x + 8 =0
=> x*(x-2) -4*(x-2) = 0
=> (x-2) * (x-4) = 0
=> x = 2 or x = 4
Method 2.2: Opening Absolute Value
| 3 - x | = 1
=> 3-x = 1 or 3-x =-1
=> x = 3-1 = 2 or x = 3+1 = 4
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
General Discussion
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Which of the following could be the value of x, if |12 − 4x|
[#permalink]
03 Apr 2020, 08:37
03 Apr 2020, 08:37
Carcass wrote:
Which of the following could be the value of x, if |12 − 4x| + 2 = 6?
A. −4
B. −2
C. 1
D. 3
E. 4
Kudos for the right answer and explanation
A. −4
B. −2
C. 1
D. 3
E. 4
Kudos for the right answer and explanation
Take: |12 − 4x| + 2 = 6
Isolate the absolute value part by subtracting 2 from both sides of the inequality: |12 − 4x| = 4
NICE RULE: If |x| = k, then x = k or x = -k
We get: 12 − 4x = 4 or 12 − 4x = -4
If 12 − 4x = 4, then x = 2.
Check the answer choices....x = 2 is not an option. Keep going.
If 12 − 4x = -4, then x = 4
Check the answer choices....bingo!
Answer: E
Cheers,
Brent
