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MathRevolution
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If |x - 6| = 2x, then x = ? 25 Oct 2018, 01:22
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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15% (low)

Question Stats:

76% (01:04) correct 24% (01:06) wrong based on 861 sessions

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If \(|x-6|=2x\), then \(x=?\)

A. -6
B. -4
C. 0
D. 2
E. 6
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D
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If |x - 6| = 2x, then x = ? 25 Oct 2018, 06:04
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MathRevolution
[Math Revolution GMAT math practice question]

If \(|x-6|=2x\), then \(x=?\)

\(A. -6\)
\(B. -4\)
\(C. 0\)
\(D. 2\)
\(E. 6\)
Show more

There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

Step 1: x - 6 = 2x or x - 6 = -2x

case a: x - 6 = 2x
Step 2: Solve to get x = -6
Step 3: Plug solution into original equation to get: |(-6) - 6| = 2(-6)
Evaluate to get: |-12| = -12 DOESN'T WORK

case b: x - 6 = -2x
Step 2: Solve to get x = 2
Step 3: Plug solution into original equation to get: |(2) - 6| = 2(2)
Evaluate to get: |-4| = 4 WORK!

Answer: D

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If |x - 6| = 2x, then x = ? 25 Oct 2018, 05:28
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MathRevolution
[Math Revolution GMAT math practice question]

If \(|x-6|=2x\), then \(x=?\)

\(A. -6\)
\(B. -4\)
\(C. 0\)
\(D. 2\)
\(E. 6\)
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2x is positive so x is positive...
|x-6|=2x
I...
x-6=2x....x=-6 but x>0, so wrong
II..
x-6=-2x....3x=6...x=2.. correct

D
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If |x - 6| = 2x, then x = ? 25 Oct 2018, 07:22
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MathRevolution
[Math Revolution GMAT math practice question]

If \(|x-6|=2x\), then \(x=?\)

\(A. -6\)
\(B. -4\)
\(C. 0\)
\(D. 2\)
\(E. 6\)
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PLUGGIN IN THE OPTIONS

(A) LHS = 12; RHS = -12 (Not equall)
(B) LHS = 10 ; RHS = -8 (Not equall)
(C) LHS = 6 ; RHS = 0 (Not equall)
(D) LHS = 4 RHS = 4 (Possible)
(E) LHS = 0 ; RHS = 12 (Not equall)

Thus, Answer must be (D)
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If |x - 6| = 2x, then x = ? 28 Oct 2018, 18:27
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MathRevolution
[Math Revolution GMAT math practice question]

If \(|x-6|=2x\), then \(x=?\)

\(A. -6\)
\(B. -4\)
\(C. 0\)
\(D. 2\)
\(E. 6\)
Show more

As with any absolute value equation, we must consider two cases:

Case 1. We solve for x when (x - 6) is positive:

x - 6 = 2x

-6 = x

Since 2(-6) = -12, and since |x - 6| cannot be -12, then -6 is not a possible value for x.

Case 2. We solve for x when (x - 6) is negative:

-(x - 6) = 2x

-x + 6 = 2x

6 = 3x

2 = x

Answer: D
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If |x - 6| = 2x, then x = ? 28 Oct 2018, 19:18
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=>

\(|x-6|=2x\)
\(=> x-6 = ±2x\)
\(=> -6 = -x ±2x\)
\(=> -6 = x\) or \(-6 = -3x\)
\(=> x = -6\) or \(x = 2\)
However, \(2x = |x-6| ≥ 0.\)
Thus, we have the unique solution \(x=2.\)


Therefore, the answer is D.
Answer: D
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If |x - 6| = 2x, then x = ? 30 Sep 2020, 23:19
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1st) Analysis of the Equation shows that X can NOT be = 0 ---- 0 will not satisfy the equation



2nd) Scenario: Quantity inside the Modulus is GREATER THAN > 0
(X - 6) > 0
X > +6 --- (Assumed Region)

Opening the Modulus:

+(X - 6) = 2x

X - 6 = 2X

X = -6

This is an INVALID Solution --- does not fall in our Assumed Range of X > +6

Plus, the OUTPUT of an Absolute Value Modulus can Never = (-)Negative

If we were to plug in X = -(6) into the R.H.S. of the Equation, the Absolute Value Modulus would = (-)Negative 12


3rd) Scenario: Quantity inside the Modulus is LESS THAN < 0

(X - 6) < 0

X < +6 ---- (Assumed Range)


Opening the Modulus:

-(X -6) = 2X

-X + 6 = 2X

6 = 3X

X = +2

This is a Valid Solution that Falls within the Assumed Range.

-D-
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If |x - 6| = 2x, then x = ? 01 Oct 2020, 02:57
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|x - 6| = 2x

=> x - 6 = 2x and x - 6 = -2x

=> x = -6 and x = 2

Substituting value of 'x = -6'

|-6 - 6| = 2(-6)

=> |-12| = -12

=> 12 ≠ -12


Substituting value of 'x = 2'

|2 - 6| = 2(2)

=> |-4| = 4

=> 4 = 4

Answer : D
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If |x - 6| = 2x, then x = ? 22 Oct 2024, 08:45
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If \(|x-6|=2x\), then \(x=?\)

A. -6
B. -4
C. 0
D. 2
E. 6

It means that x > 0 since LHS is an absolute value.

Only D and E since others are not suitable.
Here D fits the bill
|-4| = 2*2 = 4

Answer D.
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If |x - 6| = 2x, then x = ? 22 Feb 2026, 14:58
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