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

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Bunuel
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Which of the following could be the graph of all values of x that sati [#permalink] New post   16 Jul 2018, 21:07
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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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Re: Which of the following could be the graph of all values of x that sati [#permalink] New post   16 Jul 2018, 22:44
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Bunuel wrote:
Which of the following could be the graph of all values of x that satisfy the inequality \(2 - 5x \leq -\frac{(6x - 5)}{3}\) ?




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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] New post   17 Jul 2018, 00:09
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Bunuel wrote:
Which of the following could be the graph of all values of x that satisfy the inequality \(2 - 5x \leq -\frac{(6x - 5)}{3}\) ?




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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
\(15x-6≥6x-5\)

Adding -6x+6 on both sides,
\(9x≥1\)

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] New post   17 Jul 2018, 06:34
Bunuel wrote:
Which of the following could be the graph of all values of x that satisfy the inequality \(2 - 5x \leq -\frac{(6x - 5)}{3}\) ?




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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.

The best answer is C.
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Re: Which of the following could be the graph of all values of x that sati [#permalink] New post   01 Jan 2021, 11:34
Since this is an inequality, how come we don't have to solve for both conditions; 1, when (2-5x) is positive, and one when (2-5x) is negative? then wouldn't we get 1/9 <= x <= 11/21?
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Re: Which of the following could be the graph of all values of x that sati [#permalink] New post   01 Mar 2022, 05:31
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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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