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26 Jul 2021, 06:15
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
93% (00:34) correct
7%
(00:41)
wrong
based on 376
sessions
History
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Not Attempted Yet
Which of the following is the complete set of solutions for x when |x - 3| = 6 ?
(A) {9}
(B) {-9, 9}
(C) {-3, 9}
(D) {3, 9}
(E) {-9, -3, 3}
(A) {9}
(B) {-9, 9}
(C) {-3, 9}
(D) {3, 9}
(E) {-9, -3, 3}
26 Jul 2021, 06:40
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Bunuel
APPROACH #1: Algebra
Key property: If |SOMETHING| = k (where k ≥ 0), then either SOMETHING = k or SOMETHING= -k
So, if |x - 3| = 6, then either x - 3 = 6 or x - 3 = -6
If x - 3 = 6, then x = 9
If x - 3 = -6, then x = -3
So, the solutions are x = 9 and x = -3
Answer: C
APPROACH #2: Test the answer choices
Is x = 9 a solution?
Plug x = 9 into the original equation to get: |9 - 3| = 6
Simplify: |6| = 6
Works!
Since x = 9 IS a solution, we can eliminate answer choice E, since it does not include x = 9 as a possible solution.
Is x = -9 a solution?
Plug x = -9 into the original equation to get: |-9 - 3| = 6
Simplify: |-12| = 6
Doesn't work.
Since x = -9 is NOT a solution, we can eliminate answer choice B, since it says x = -9 is a possible solution.
Is x = -3 a solution?
Plug x = -3 into the original equation to get: |-3 - 3| = 6
Simplify: |-6| = 6
Works!
Since x = -3 IS a solution, we can eliminate answer choice A and D, since they don.t include x = -3 as a possible solution.
Answer: C
General Discussion
26 Jul 2021, 10:02
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Solution:
We know if we have \(|x-a|\) we can have 2 cases and those are:
Similarly, \(|x - 3| = 6\) can also have 2 cases:
Thus x can have 2 values: \(9\) and \(-3\).
Hence the right answer is Option C.
We know if we have \(|x-a|\) we can have 2 cases and those are:
- Case 1: \(x-a\) (such that \(x≥a\))
- Case 2: \(-(x-a)\) (such that \(x<a\))
Similarly, \(|x - 3| = 6\) can also have 2 cases:
- Case 1: \(x-3=6⇒x=9\) (such that \(x≥3\))
- Case 2: \(-(x-3)=6⇒x=-3\) (such that \(x<3\))
Thus x can have 2 values: \(9\) and \(-3\).
Hence the right answer is Option C.
