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

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Math Expert
Joined: 02 Sep 2009
Posts: 50671
If 2(x – 1)^3 + 3 >= 19, which of the following must be true?  [#permalink]

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23 Jul 2018, 19:35
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Difficulty:

5% (low)

Question Stats:

90% (01:08) correct 10% (01:20) wrong based on 41 sessions

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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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Updated on: 23 Jul 2018, 20:20
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, 19:55.
Last edited by Akash720 on 23 Jul 2018, 20:20, edited 2 times in total.
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Posts: 1005
Concentration: Nonprofit
GPA: 4
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Re: If 2(x – 1)^3 + 3 >= 19, which of the following must be true?  [#permalink]

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23 Jul 2018, 20:16
2
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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Updated on: 23 Jul 2018, 20:32
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, 20:17.
Last edited by selim on 23 Jul 2018, 20:32, 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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23 Jul 2018, 20:19
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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23 Jul 2018, 20:22
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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23 Jul 2018, 20:50
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, 20:50
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