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Which of the following is the complete set of solutions for x when |x

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Which of the following is the complete set of solutions for x when |x [#permalink] New post   20 Dec 2021, 01:34
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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}
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C
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Re: Which of the following is the complete set of solutions for x when |x [#permalink] New post   20 Dec 2021, 06:44
Carcass wrote:
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}


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
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Which of the following is the complete set of solutions for x when |x [#permalink] New post   30 Dec 2021, 20:46
Given that |x - 3| = 6 and we need to find the value of x

Let's solve this using two methods

Method 1: Substitution

Let's take values in the option choices and plug it in the equation and check if it satisfies the equation

-9 -> Put x = -9 in |x - 3| = 6 and check if it satisfies the equation
=> | -9 -3| = |-12| = 12 \(\neq\) 6 => NOT POSSIBLE

-3 -> Put x = -3 in |x - 3| = 6 and check if it satisfies the equation
=> | -3 -3| = |-6| = 6 = 6 => POSSIBLE

3 -> Put x = 3 in |x - 3| = 6 and check if it satisfies the equation
=> | 3 -3| = |0| = 0 \(\neq\) 6 => NOT POSSIBLE

9 -> Put x = 9 in |x - 3| = 6 and check if it satisfies the equation
=> | 9 -3| = |6| = 6 = 6 => POSSIBLE
So, x = { -3 , 9 }

Method 2: Algebra

|x - 3| = 6
=> x-3 = 6 or x-3 = -6
=> x = 6+3 or x = -6 + 3
=> x = 9 or -3

So, Answer will be C
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

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Re: Which of the following is the complete set of solutions for x when |x [#permalink] New post   08 Jul 2024, 15:18
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