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3 |x - 4| = 16

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Carcass
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3 |x - 4| = 16 [#permalink] New post   23 Jul 2018, 09:36
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\(3 |x - 4| = 16\)

Quantity A
Quantity B
\(x\)
\(\frac{28}{3}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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GreenlightTestPrep
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Re: 3 |x - 4| = 16 [#permalink] New post   12 Aug 2018, 07:40
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Carcass wrote:
\(3 |x - 4| = 16\)

Quantity A
Quantity B
\(x\)
\(\frac{28}{3}\)



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

GIVEN: 3|x - 4| = 16
Divide both sides by 3 to get: |x - 4| = 16/3
Based on the above rule, we get TWO possible equations: x - 4 = 16/3 and x - 4 = -16/3

Let's solve each equation...
Take: x - 4 = 16/3
Add 4 to both sides to get: x = 16/3 + 4
Rewrite with common denominator: x = 16/3 + 12/3
Combine fractions to get: x = 28/3
In this case, the two quantities are EQUAL

Take: x - 4 = -16/3
Add 4 to both sides to get: x = -16/3 + 4
Rewrite with common denominator: x = -16/3 + 12/3
Combine fractions to get: x = -4/3
In this case, the two Quantity B IS GREATER

Answer: D
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mariogarciaLA
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3 |x - 4| = 16 [#permalink] New post   27 Feb 2023, 23:11
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The trap here is C (both values being 28 / 3) for students who don't test both the positive and negative cases.
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HarishKumar
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3 |x - 4| = 16 [#permalink] New post   20 Jun 2023, 01:08
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\(3|x-4| =16\)

\(|x-4| = \frac{16}{3}\)

Now, you can write two equations,

because \(|(x-4)| = |-(x-4)| \)

Therefore,

The first equation

\(x-4 = \frac{16}{3}\)

\(x=\frac{16}{3}+4\)

\(x=\frac{16+12}{3}\)

\(x=\frac{28}{3}\)

Both Quantities are Equal and therefore Choice is C.

The second equation

\(-(x-4) = \frac{16}{3}\)

\(-x+4 = \frac{16}{3}\)

\(-x = \frac{16}{3} - 4\)

\(-x = \frac{16-12}{3}\)

\(-x = \frac{4}{3}\)

\(x = -\frac{4}{3}\)

Quantity B is greater than Quantity A. Therefore, Choice B is true.

Since both equations lead to different results, the relationship cannot be determined and D is the correct answer.
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Re: 3 |x - 4| = 16 [#permalink] New post   23 Aug 2025, 06:48
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: 3 |x - 4| = 16 [#permalink]
23 Aug 2025, 06:48
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