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# If |3x - 2 + 4x| > 7, which of the following is a possible

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Director
Joined: 07 Jan 2018
Posts: 659
Followers: 7

Kudos [?]: 615 [1] , given: 88

If |3x - 2 + 4x| > 7, which of the following is a possible [#permalink]  28 Apr 2018, 00:45
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Question Stats:

57% (01:28) correct 42% (01:48) wrong based on 7 sessions
If $$|3x - 2 + 4x| > 7$$, which of the following is a possible value for x?

A. $$-\frac{2}{3}$$

B. $$-\frac{1}{2}$$

C. $$\frac{3}{4}$$

D. $$\frac{5}{4}$$

E. $$\frac{4}{3}$$
[Reveal] Spoiler: OA
Manager
Joined: 26 Jan 2018
Posts: 186
Followers: 0

Kudos [?]: 115 [0], given: 3

Re: If |3x - 2 + 4x| > 7, which of the following is a possible [#permalink]  04 May 2018, 04:43
Given the equation, the value of x has to be greater than 1 to satisfy the condition. So it could be 1 of the last 2 options. On plugging we would know it is the last option.
Director
Joined: 07 Jan 2018
Posts: 659
Followers: 7

Kudos [?]: 615 [0], given: 88

Re: If |3x - 2 + 4x| > 7, which of the following is a possible [#permalink]  09 May 2018, 23:48
Since the given equation is inside a modulus.
We have to take two cases while solving the equation
1st,
3x - 2 + 4x > 7
or, 7x>9
or,$$x > \frac{9}{7}$$

2nd,
3x - 2 + 4x < -7 (when multiplying both sides by -1 the inequality sign reverses)
or, 7x< -5
or, $$x < \frac{-5}{7}$$

therefore,
only option E falls withing the range since this is greater than $$\frac{9}{7}$$
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Re: If |3x - 2 + 4x| > 7, which of the following is a possible   [#permalink] 09 May 2018, 23:48
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