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If 2(x – 1)^3 + 3 >= 19, which of the following must be true?

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If 2(x – 1)^3 + 3 >= 19, which of the following must be true?  [#permalink]

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New post 23 Jul 2018, 20:35
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Question Stats:

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If \(2(x – 1)^3 + 3 \geq 19\), which of the following must be true?


(A) \(x \leq 3\)

(B) \(x \geq 3\)

(C) \(x \leq - 3\)

(D) \(x \geq - 3\)

(E) \(x < - 3\) or \(x > 3\)

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If 2(x – 1)^3 + 3 >= 19, which of the following must be true?  [#permalink]

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New post Updated on: 23 Jul 2018, 21:20
Bunuel wrote:
If \(2(x – 1)^3 + 3 \geq 19\), which of the following must be true?


(A) \(x \leq 3\)

(B) \(x \geq 3\)

(C) \(x \leq - 3\)

(D) \(x \geq - 3\)

(E) \(x < - 3\) or \(x > 3\)


Just substitute values in the equation.

If x = 1 - Doesn't satisfy
x = -1 - Doesn't satisfy
x = 2 - Doesn't satisfy
x = -2 - Doesn't satisfy
x = 3 - Satisfies
x = -3 - Doesn't satisfy

So when x is greater than or equal to 3 equation satisfies, From options B
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Originally posted by Akash720 on 23 Jul 2018, 20:55.
Last edited by Akash720 on 23 Jul 2018, 21:20, edited 2 times in total.
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Re: If 2(x – 1)^3 + 3 >= 19, which of the following must be true?  [#permalink]

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New post 23 Jul 2018, 21:16
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Bunuel wrote:
If \(2(x – 1)^3 + 3 \geq 19\), which of the following must be true?


\(2(x – 1)^3 + 3 \geq 19\)

=> \(2(x – 1)^3 \geq 16\)

=> \((x – 1)^3 \geq 8\)

=> \((x – 1)^3 \geq 2^3\)

=> \(x-1 \geq 2\)

=> \(x \geq 3\)

Hence option B
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If 2(x – 1)^3 + 3 >= 19, which of the following must be true?  [#permalink]

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New post Updated on: 23 Jul 2018, 21:32
Bunuel wrote:
If \(2(x – 1)^3 + 3 \geq 19\), which of the following must be true?


(A) \(x \leq 3\)

(B) \(x \geq 3\)

(C) \(x \leq - 3\)

(D) \(x \geq - 3\)

(E) \(x < - 3\) or \(x > 3\)



Given

\(2(x – 1)^3 + 3 \geq 19\)

\(2(x-1)^3 >= 16\)

\((x-1)^3 >= 8\)

\((x-1)^3 >= 2^3\)

x-1 >= 2

x>=3

Thus the best answer is B.

Originally posted by selim on 23 Jul 2018, 21:17.
Last edited by selim on 23 Jul 2018, 21:32, edited 2 times in total.
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Re: If 2(x – 1)^3 + 3 >= 19, which of the following must be true?  [#permalink]

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New post 23 Jul 2018, 21:19
Akash720 wrote:
Bunuel wrote:
If \(2(x – 1)^3 + 3 \geq 19\), which of the following must be true?


(A) \(x \leq 3\)

(B) \(x \geq 3\)

(C) \(x \leq - 3\)

(D) \(x \geq - 3\)

(E) \(x < - 3\) or \(x > 3\)


Just substitute values in the equation.

If x = 1 - Doesn't satisfy
x = -1 - Satisfies
x = 2 - Doesn't satisfy
x = -2 - Satisfies
x = 3 - Satisfies
x = -3 - Satisfies

So when x < -1 and x > 3 equation satisfies, From options E



As the exponent is odd , x can't be negative. Otherwise , negative value can't be greater than 8 or 16. Thanks.
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Re: If 2(x – 1)^3 + 3 >= 19, which of the following must be true?  [#permalink]

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New post 23 Jul 2018, 21:22
selim wrote:
Akash720 wrote:
Bunuel wrote:
If \(2(x – 1)^3 + 3 \geq 19\), which of the following must be true?


(A) \(x \leq 3\)

(B) \(x \geq 3\)

(C) \(x \leq - 3\)

(D) \(x \geq - 3\)

(E) \(x < - 3\) or \(x > 3\)


Just substitute values in the equation.

If x = 1 - Doesn't satisfy
x = -1 - Satisfies
x = 2 - Doesn't satisfy
x = -2 - Satisfies
x = 3 - Satisfies
x = -3 - Satisfies

So when x < -1 and x > 3 equation satisfies, From options E



As the exponent is odd , x can't be negative. Otherwise , negative value can't be greater than 8 or 16. Thanks.


Thanks for pointing out selim careless mistake from my side
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Re: If 2(x – 1)^3 + 3 >= 19, which of the following must be true?  [#permalink]

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New post 23 Jul 2018, 21:50
B it is !

If 2(x – 1)^3 + 3 >= 19

when you solve through the inequalities you get

(x-1)^3 >= 8

x >= 3
Re: If 2(x – 1)^3 + 3 >= 19, which of the following must be true? &nbs [#permalink] 23 Jul 2018, 21:50
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