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3 |x - 4| = 16

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3 |x - 4| = 16 [#permalink] New post 23 Jul 2018, 09:36
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Question Stats:

65% (00:48) correct 34% (00:32) wrong based on 35 sessions
\(3 |x - 4| = 16\)

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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[Reveal] Spoiler: OA

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Re: 3 |x - 4| = 16 [#permalink] New post 12 Aug 2018, 07:40
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Expert's post
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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Re: 3 |x - 4| = 16   [#permalink] 12 Aug 2018, 07:40
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