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# Which of the following, if solved, would yield the set of all real num

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Math Expert
Joined: 02 Sep 2009
Posts: 56266
Which of the following, if solved, would yield the set of all real num  [#permalink]

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10 Aug 2018, 03:46
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Difficulty:

25% (medium)

Question Stats:

70% (01:08) correct 30% (01:37) wrong based on 170 sessions

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Which of the following, if solved, would yield the set of all real numbers that are exactly 15 units away from -3?

A. |x + 3| = 15
B. |x - 3| = 15
C. |x - 15| = 3
D. |x + 15| = 3
E. |x + 15| = -3

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Re: Which of the following, if solved, would yield the set of all real num  [#permalink]

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10 Aug 2018, 04:30
Bunuel wrote:
Which of the following, if solved, would yield the set of all real numbers that are exactly 15 units away from -3?

A. |x + 3| = 15
B. |x - 3| = 15
C. |x - 15| = 3
D. |x + 15| = 3
E. |x + 15| = -3

Set of all real numbers that are exactly 15 units away from -3

Implies that the set contains (-3-15) and (-3+15) as its elements.
So, x=-18 and -12
A. $$\left|x+3\right|=15$$
So, x+3=15 or -(x+3)=15
Or, x=12 , x+3=-15 or, x=-15-3=-18

Ans. (A)
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Re: Which of the following, if solved, would yield the set of all real num  [#permalink]

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10 Aug 2018, 04:36
Bunuel wrote:
Which of the following, if solved, would yield the set of all real numbers that are exactly 15 units away from -3?

A. |x + 3| = 15
B. |x - 3| = 15
C. |x - 15| = 3
D. |x + 15| = 3
E. |x + 15| = -3

15 units away from -3 = -3+15=12 and -3-15=-18

in A we have
x+3=15
x=12

and

-x-3=15
x=-18

A it is
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Re: Which of the following, if solved, would yield the set of all real num  [#permalink]

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10 Aug 2018, 05:05
Bunuel wrote:
Which of the following, if solved, would yield the set of all real numbers that are exactly 15 units away from -3?

-3 + 15 = 12 ( Positive side of line )
-3 - 15 = -18 ( Negative side of line )

Option A:
|x + 3| = 15

Case 1:
x + 3 = 15
x = 12

Case 2:
-x - 3 = 15
x = -18

Hence, A.
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Re: Which of the following, if solved, would yield the set of all real num   [#permalink] 10 Aug 2018, 05:05
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