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# 2x + 1 > 3x + 2 and 5x + 2 > 4x

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2x + 1 > 3x + 2 and 5x + 2 > 4x [#permalink]  17 Sep 2018, 20:29
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Question Stats:

82% (00:44) correct 17% (01:08) wrong based on 39 sessions

$$2x + 1 > 3x$$ + 2 and $$5x + 2 > 4x$$

 Quantity A Quantity B x 1

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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VP
Joined: 20 Apr 2016
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WE: Engineering (Energy and Utilities)
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Re: 2x + 1 > 3x + 2 and 5x + 2 > 4x [#permalink]  17 Sep 2018, 22:15
1
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Carcass wrote:
$$2x + 1 > 3x$$ + 2 and $$5x + 2 > 4x$$

 Quantity A Quantity B x 1

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

$$2x + 1 > 3x + 2$$

or $$x < -1$$

$$5x + 2 > 4x$$

or $$x > -2$$

Therefore $$-2 < x < -1$$

So, QTY A < QTY B
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Re: 2x + 1 > 3x + 2 and 5x + 2 > 4x [#permalink]  20 Sep 2018, 12:52
1
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Expert's post
Carcass wrote:
$$2x + 1 > 3x$$ + 2 and $$5x + 2 > 4x$$

 Quantity A Quantity B x 1

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Turns out that we can solve this with only the first inequality: 2x + 1 > 3x + 2

Take: 2x + 1 > 3x + 2
Subtract 2x from both sides: 1 > x + 2
Subtract 2 from both sides: -1 > x

Since x is less than -1, we can be certain that x is less than 1

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Re: 2x + 1 > 3x + 2 and 5x + 2 > 4x   [#permalink] 20 Sep 2018, 12:52
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# 2x + 1 > 3x + 2 and 5x + 2 > 4x

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