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# Which of the following could be the graph of all values of x that sati

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Math Expert
Joined: 02 Sep 2009
Posts: 50711
Which of the following could be the graph of all values of x that sati  [#permalink]

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16 Jul 2018, 20:07
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Difficulty:

15% (low)

Question Stats:

78% (01:30) correct 22% (01:26) wrong based on 94 sessions

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Which of the following could be the graph of all values of x that satisfy the inequality $$2 - 5x \leq -\frac{(6x - 5)}{3}$$ ?

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Quant.jpg [ 13.54 KiB | Viewed 924 times ]

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Re: Which of the following could be the graph of all values of x that sati  [#permalink]

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16 Jul 2018, 21:44
Bunuel wrote:
Which of the following could be the graph of all values of x that satisfy the inequality $$2 - 5x \leq -\frac{(6x - 5)}{3}$$ ?

Attachment:
Quant.jpg

Option A, B, and D have the point x=0 in common.

At x=0, we have LHS=2, RHS=5/3, so the given inequality is not valid.
So, option A,B, and D are eliminated.

Between C & E, E possesses negative value of x.
At x=-2, LHS=12 and RHS=17/3; so the given inequality is not valid. Option E is eliminated.

Ans. (C)

P.S:- By solving the inequality, we have $$x\geq{\frac{1}{9}}$$. Straightaway option (C).
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Re: Which of the following could be the graph of all values of x that sati  [#permalink]

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16 Jul 2018, 23:09
Bunuel wrote:
Which of the following could be the graph of all values of x that satisfy the inequality $$2 - 5x \leq -\frac{(6x - 5)}{3}$$ ?

Attachment:
Quant.jpg

OA:C
$$2 - 5x \leq -\frac{(6x - 5)}{3}$$

Multilpying both sides by -1, we get
$$5x-2≥ \frac{{6x-5}}{3}$$

Multiplying both sides by 3 , we get
$$15x-6≥6x-5$$

$$9x≥1$$

Dividing by 9 on both sides
$$x≥\frac{1}{9}$$

Only C satisifies this condition
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Re: Which of the following could be the graph of all values of x that sati  [#permalink]

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17 Jul 2018, 05:34
Bunuel wrote:
Which of the following could be the graph of all values of x that satisfy the inequality $$2 - 5x \leq -\frac{(6x - 5)}{3}$$ ?

Attachment:
Quant.jpg

Given

$$2 - 5x \leq -\frac{(6x - 5)}{3}$$

6 - 15x <= - 6x -5

15 x -6 >= 6x -5

9x >= 1

x >= 1/9.

Only option C fits the condition.

Re: Which of the following could be the graph of all values of x that sati &nbs [#permalink] 17 Jul 2018, 05:34
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