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If x = −2, which of the following is(are) false?

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If x = −2, which of the following is(are) false?  [#permalink]

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New post Updated on: 06 Dec 2019, 08:31
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A
B
C
D
E

Difficulty:

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Question Stats:

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If x = −2, which of the following is(are) false?

(I) |x| = −|x| + |2x|
(II) (x) ^(− x) = (−x)^x
(III) (−x)^0=−x/|x|
(IV) (1/x)^|x|=|x|^x

A: I and II
B: II and III
C: III and IV
D: II, III and IV
E : Only II

Originally posted by JiddiHuMain on 06 Dec 2019, 07:24.
Last edited by JiddiHuMain on 06 Dec 2019, 08:31, edited 1 time in total.
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Re: If x = −2, which of the following is(are) false?  [#permalink]

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New post 06 Dec 2019, 07:45
Top Contributor
JiddiHuMain wrote:
If x = −2, which of the following is(are) false?

(I) |x| = −|x| + |2x|
(II) (x) − x = (−x)x
(III) (−x)⁰ = −x|x|
(IV) (1/x)|x| = |x|x

A: I and II
B: II and III
C: III and IV
D: II, III and IV
E : Only II


Plug x = −2 into each statement to get:
(I) |−2| = −|−2| + |2(−2)|
Simplify: 2 = -(2) + |-4|
Simplify: 2 = -2 + 4
Simplify: 2 = 2
TRUE

(II) (−2) − −2 =(−(−2))(−2)
Simplify: 0 = (2)(-2)
Simplify: 0 = -4
FALSE

(III) (−(−2))⁰ = −(−2)|−2|
Simplify: 1 = (2)(2)
Simplify: 1 = 4
FALSE

(IV) (1/(−2))|−2| = |−2|(−2)
Simplify: (-0.5)(2) = (2)(-2)
Simplify: -1 = -4
FALSE

Answer: D

Cheers.
Brent
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If x = −2, which of the following is(are) false?  [#permalink]

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New post 06 Dec 2019, 08:28
1
Solution :

As we know | x | = x if x ≥ 0
= −x if x < 0

Given x = −2 ⇒ |x| = |−2| = 2

Considering statement I :-

|x| = −|x| + |2x|

LHS = |x| = 2

RHS = −|x| + |2x| = −(2) + |−4| = −2 + 4 = 2

Since LHS = RHS ⇒ I is true

Considering statement II:-

(x)−x = (−x)x

LHS = (x)−x = (−2)−(−2) = (−2)2 = 4

RHS = (−x)x = (2)(−2) = 1/4

Since LHS is not equal to RHS ⇒ II is False

Considering statement III:-

(-x)0 = −x/|x|

LHS = {-(-2)}0 = (2)0 = 1

RHS = -x/|x| = −(−2)/(2) = 1

Since LHS = RHS ⇒ III is True

Considering statement IV:-

(1/x)|x| = |x|x

LHS = (1/x)|x| = (−1/2)(2) = 1/4

RHS = |x|x = (2)(−2) = 1/4

Since LHS = RHS ⇒ IV is also True.

Therefore, only statement II is false

Answer: E.
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If x = −2, which of the following is(are) false?  [#permalink]

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New post 06 Dec 2019, 09:10
Top Contributor
1
JiddiHuMain wrote:
Solution :


In the future, if you change the wording of your original post after someone (e.g., me) has posted a solution, please add something to the thread to indicate that you've made such a change.
As you can see in my solution, the original question had different expressions for statements III and IV
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If x = −2, which of the following is(are) false?   [#permalink] 06 Dec 2019, 09:10
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