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What is the value of x? (1) |x + 5| = |x + 3| (2) |x + 3| = 1
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05 May 2021, 05:30
05 May 2021, 05:30
2
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Expert Reply
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00:00
A
B
C
D
E
Difficulty:
35%
(medium)
Question Stats:
65% (01:22) correct
35%
(01:32)
wrong
based on 97
sessions
Re: What is the value of x? (1) |x + 5| = |x + 3| (2) |x + 3| = 1
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16 May 2021, 11:26
16 May 2021, 11:26
Expert Reply
What is the value of x?
(1) |x+5| = |x+3| --> square both sides: (x+5)^2=(x+3)^2 --> x^2+10 x+25 = x^2+6 x+9 --> 4x=-16 --> x=-4 . Sufficient.
(2) |x+3| = 1 --> x + 3 = 1 or x + 3 = -1. Hence, x = -2 or x = -4. Not sufficient.
Answer: A.
(1) |x+5| = |x+3| --> square both sides: (x+5)^2=(x+3)^2 --> x^2+10 x+25 = x^2+6 x+9 --> 4x=-16 --> x=-4 . Sufficient.
(2) |x+3| = 1 --> x + 3 = 1 or x + 3 = -1. Hence, x = -2 or x = -4. Not sufficient.
Answer: A.
General Discussion
Re: What is the value of x? (1) |x + 5| = |x + 3| (2) |x + 3| = 1
[#permalink]
05 May 2021, 05:41
05 May 2021, 05:41
Expert Reply
Bunuel wrote:
What is the value of x?
(1) |x+ 5| = |x + 3|
(2) |x + 3| = 1
(1) |x+ 5| = |x + 3|
(2) |x + 3| = 1
(1) |x+ 5| = |x + 3|
Square both sides as both are non negative
\(x^2+10x+25=x^2+6x+9...........4x=-16.......x=-4\).
OR Number line: x us equidistant from -5 and -3. It has to be -4
Sufficient
(2) |x + 3| = 1
x could be -2 or -4
OR Number line: x is 1 unit away from -3. It has to be -2 or -4
Insufficient
A
