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3 |x - 4| = 16
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23 Jul 2018, 09:36
23 Jul 2018, 09:36
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Question Stats:
69% (01:00) correct
30% (00:57) wrong based on 204 sessions
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\(3 |x - 4| = 16\)
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.
Kudos for R.A.E
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.
Kudos for R.A.E
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Re: 3 |x - 4| = 16
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12 Aug 2018, 07:40
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
General Discussion
3 |x - 4| = 16
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27 Feb 2023, 23:11
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.
