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

Question

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

sudarshan22 · Accepted Answer

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

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

Hence,   C  .

adkikani · Answer

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

gmatbusters   VeritasKarishma   Gladiator59   Abhishek009   chetan2u

PKN · Answer

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)

Ritz123 · Answer

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?

PKN · Answer

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.

CLIMBTHELADDER · Answer

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.

GMATBusters · Answer

adkikani

You are right.

Posted from my mobile device

Gladiator59 · Answer

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, Gladi

KarishmaB · Answer

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

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

Prep Toolkit

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