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Math Expert V
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If |4x - 7| = |3x + 2|, which of the following is a possible value of  [#permalink]

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Difficulty:   5% (low)

Question Stats: 82% (01:34) correct 18% (01:52) wrong based on 344 sessions

HideShow timer Statistics If |4x - 7| = |3x + 2|, which of the following is a possible value of x?

A. -2
B. 1
C. 5/7
D. 7/5
E. 3

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If |4x - 7| = |3x + 2|, which of the following is a possible value of  [#permalink]

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Bunuel wrote:
If |4x - 7| = |3x + 2|, which of the following is a possible value of x?

A. -2
B. 1
C. 5/7
D. 7/5
E. 3

Given, |4x - 7| = |3x + 2|
Squaring both sides,

$$(4x - 7)^2 = (3x + 2)^2$$
Or, $$16x^2-56x+49=9x^2+4+12x$$
Or, $$7x^2-68x+45=0$$
Or, $$x^2-\frac{68}{7}x+\frac{45}{7}=0$$
Or, $$(x-\frac{5}{7})(x-9)=0$$
Or, $$x=\frac{5}{7} or, x=9$$

Ans. (C)
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Originally posted by PKN on 10 Aug 2018, 03:57.
Last edited by PKN on 10 Aug 2018, 04:50, edited 1 time in total.
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Re: If |4x - 7| = |3x + 2|, which of the following is a possible value of  [#permalink]

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Bunuel wrote:
If |4x - 7| = |3x + 2|, which of the following is a possible value of x?

Case 1 :
4x - 7 = 3x + 2
x = 9 (Not in option)

Case 2 :
4x - 7 = -3x - 2
7x = 5
x = 5 / 7

Hence, C.
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Re: If |4x - 7| = |3x + 2|, which of the following is a possible value of  [#permalink]

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Should we not substitute the value back in the modulus and confirm whether the solution holds true? It holds true for x=9 but not for x=5/7.
Am I missing something?
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Re: If |4x - 7| = |3x + 2|, which of the following is a possible value of  [#permalink]

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Ritz123 wrote:
Should we not substitute the value back in the modulus and confirm whether the solution holds true? It holds true for x=9 but not for x=5/7.
Am I missing something?

Hi Ritz123,
Since the equation deals with only absolute function, you needn't to check the solution by substitution.
At x=$$\frac{5}{7}$$, LHS: $$|4x-7|=|4*\frac{5}{7}-7|=|\frac{20}{7}-7|$$=$$|\frac{20-49}{7}|$$=$$|\frac{-29}{7}|$$=$$\frac{29}{7}$$

RHS: $$|3x+2|=|3*\frac{5}{7}+2|=|\frac{15}{7}+2|=|\frac{15+14}{7}|=|\frac{29}{7}|=\frac{29}{7}$$

LHS=RHS.
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Re: If |4x - 7| = |3x + 2|, which of the following is a possible value of  [#permalink]

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Here's how I got to the right answer choice.

l 4x - 7 l = - l 3x+2 l or l 4x-7 l = l 3x +2 l

If we try to calculate the x for the first case, we find that x = 5/7, which is one of the possible answer choices. Hence, C.
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Re: If |4x - 7| = |3x + 2|, which of the following is a possible value of  [#permalink]

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Bunuel wrote:
If |4x - 7| = |3x + 2|, which of the following is a possible value of x?

A. -2
B. 1
C. 5/7
D. 7/5
E. 3
.

Hello Bunuel

Could you post detail solution for this question.

Thanks,
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If |4x - 7| = |3x + 2|, which of the following is a possible value of  [#permalink]

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ammuseeru

One of efficient ways of solving modulus on both sides is below approach:

|a| = |b| reduces to
a = b or a = -b

hence the problem becomes:
4x-7 = 3x+2
or x=9

Or
4x-7 = -3x-2
or 7x = 5
or x=5/7

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Re: If |4x - 7| = |3x + 2|, which of the following is a possible value of  [#permalink]

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You are right.

ammuseeru

One of efficient ways of solve modulus on both sides is below approach:

|a| = |b| reduces to
a = b or a = -b

hence the problem becomes:
4x-7 = 3x+2
or x=9

Or
4x-7 = -3x-2
or 7x = 5
or x=5/7

Posted from my mobile device
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GMAT 1: 740 Q50 V40 GMAT 2: 770 Q51 V42 Re: If |4x - 7| = |3x + 2|, which of the following is a possible value of  [#permalink]

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This would be the fastest approach. Good work adkikani Another longer approach would be squaring both sides and solving the quadratic to get two solutions. I would recommend solving by that approach as well to get a better understanding of such questions.

Regards,

ammuseeru

One of efficient ways of solving modulus on both sides is below approach:

|a| = |b| reduces to
a = b or a = -b

hence the problem becomes:
4x-7 = 3x+2
or x=9

Or
4x-7 = -3x-2
or 7x = 5
or x=5/7

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Regards,

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Re: If |4x - 7| = |3x + 2|, which of the following is a possible value of  [#permalink]

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ammuseeru

One of efficient ways of solving modulus on both sides is below approach:

|a| = |b| reduces to
a = b or a = -b

hence the problem becomes:
4x-7 = 3x+2
or x=9

Or
4x-7 = -3x-2
or 7x = 5
or x=5/7

Yes, this is the approach using the concept of absolute values. Though in these questions, I feel squaring both sides is faster. Since it is absolute value on both sides, no negative values are possible. So even if we are dealing with inequalities, it doesn't matter.
Given |a| = |b|, you can safely say that a^2 = b^2
Given |a| < |b|, you can safely say that a^2 < b^2
Given |a| > |b|, you can safely say that a^2 > b^2
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Veritas Prep GMAT Instructor Re: If |4x - 7| = |3x + 2|, which of the following is a possible value of   [#permalink] 01 Jan 2019, 03:49
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