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If |-3x + 1| < 7, then which of the following represents all possible

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If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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New post 13 Jul 2018, 00:01
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If \(|-3x + 1| < 7\), then which of the following represents all possible values of x?


A. \(-2 < x\)

B. \(-2 < x < \frac{8}{3}\)

C. \(-2 \leq x \leq \frac{8}{3}\)

D. \(x < -2\) or \(x > \frac{8}{3}\)

E. \(x \leq -2\) or \(x \geq \frac{8}{3}\)

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Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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New post 13 Jul 2018, 00:09
2
Bunuel wrote:
If |-3x + 1| < 7, then which of the following represents all possible values of x?

A. -2 < x
B. -2 < x < 8/3
C. -2 < x < 8/3
D. x < -2 or x > 8/3
E. x < -2 or x < 8/3



since there is only one MOD, we can take the best method of opening MOD here
so two cases
|-3x+1|<7.............-3x+1<7...............-3x<6..................-x<2 or x>-2

|-3x+1|<7.............-(-3x+1)<7...............3x-1<7..................3x<8 or x<8/3

so -2<x<8/3

B or C

Bunuel both B and C are same .. some typo
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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New post 13 Jul 2018, 00:18
chetan2u wrote:
Bunuel wrote:
If |-3x + 1| < 7, then which of the following represents all possible values of x?

A. -2 < x
B. -2 < x < 8/3
C. -2 < x < 8/3
D. x < -2 or x > 8/3
E. x < -2 or x < 8/3



since there is only one MOD, we can take the best method of opening MOD here
so two cases
|-3x+1|<7.............-3x+1<7...............-3x<6..................-x<2 or x>-2

|-3x+1|<7.............-(-3x+1)<7...............3x-1<7..................3x<8 or x<8/3

so -2<x<8/3

B or C

Bunuel both B and C are same .. some typo


Edited. Thank you for noticing.
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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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New post 13 Jul 2018, 02:29
Bunuel wrote:
If \(|-3x + 1| < 7\), then which of the following represents all possible values of x?


A. \(-2 < x\)

B. \(-2 < x < \frac{8}{3}\)

C. \(-2 \leq x \leq \frac{8}{3}\)

D. \(x < -2\) or \(x > \frac{8}{3}\)

E. \(x \leq -2\) or \(x \geq \frac{8}{3}\)



Case 1 : (-3x + 1) is positive .

( -3x + 1) <7
-3x < 6
-x < 2
x> -2.

Case 2: ( -3x +1 ) is negative :

- (-3x + 1) <7
3x -1 <7
x < 8/3.

Combining both cases :

-2 <x < 8/3.

Option B fits .


The best answer is B.
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If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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New post 19 Sep 2018, 18:53
chetan2u wrote:
Bunuel wrote:
If |-3x + 1| < 7, then which of the following represents all possible values of x?

A. -2 < x
B. -2 < x < 8/3
C. -2 < x < 8/3
D. x < -2 or x > 8/3
E. x < -2 or x < 8/3



since there is only one MOD, we can take the best method of opening MOD here
so two cases
|-3x+1|<7.............-3x+1<7...............-3x<6..................-x<2 or x>-2

|-3x+1|<7.............-(-3x+1)<7...............3x-1<7..................3x<8 or x<8/3

so -2<x<8/3

B or C

Bunuel both B and C are same .. some typo


Hi chetan2u,

While solving the above, i tried to get the solutions with the following

-7<-3x+1<7

is this wrong?

Thanks
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Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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New post 19 Sep 2018, 19:13
Amirfunc wrote:
chetan2u wrote:
Bunuel wrote:
If |-3x + 1| < 7, then which of the following represents all possible values of x?

A. -2 < x
B. -2 < x < 8/3
C. -2 < x < 8/3
D. x < -2 or x > 8/3
E. x < -2 or x < 8/3



since there is only one MOD, we can take the best method of opening MOD here
so two cases
|-3x+1|<7.............-3x+1<7...............-3x<6..................-x<2 or x>-2

|-3x+1|<7.............-(-3x+1)<7...............3x-1<7..................3x<8 or x<8/3

so -2<x<8/3

B or C

Bunuel both B and C are same .. some typo


Hi chetan2u,

While solving the above, i tried to get the solutions with the following

-7<-3x+1<7

is this wrong?

Thanks



This is also correct..
-7<-3x+1<7
-7-1<-3x<7-1
-8<-3x<6
8>3x>6
8/3>x>-2
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Director
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Re: If |–3x + 1| < 7, then which of the following represents all possible  [#permalink]

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New post 31 Oct 2018, 00:20
Bunuel wrote:
If |–3x + 1| < 7, then which of the following represents all possible values of x?


A. −2 < x

B. −2 < x < 8/3

C. –2 ≤ x ≤ 8/3

D. x < −2, or x > 8/3

E. x ≤ –2, or x ≥ 8/3



Case 1:

| (-3x + 1) <7

- 3x + 1 < 7

x> -2

Case 2:

|–3x + 1| < 7

3x -1 <7

x < 8/3


-2 <x<8/3

The best answer is B.
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If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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New post 31 Oct 2018, 01:00
1
Bunuel wrote:
If \(|-3x + 1| < 7\), then which of the following represents all possible values of x?


A. \(-2 < x\)

B. \(-2 < x < \frac{8}{3}\)

C. \(-2 \leq x \leq \frac{8}{3}\)

D. \(x < -2\) or \(x > \frac{8}{3}\)

E. \(x \leq -2\) or \(x \geq \frac{8}{3}\)


Another method is to use the distance concept of absolute values.

\(|-3x + 1| < 7\)

\(3|-x + 1/3| < 7\)

\(|x - 1/3| < 7/3\)

-2 < x< 8/3

Answer (B)

For more, check:
https://www.veritasprep.com/blog/2011/0 ... edore-did/
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Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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New post 31 Oct 2018, 06:08
Top Contributor
Bunuel wrote:
If \(|-3x + 1| < 7\), then which of the following represents all possible values of x?


A. \(-2 < x\)

B. \(-2 < x < \frac{8}{3}\)

C. \(-2 \leq x \leq \frac{8}{3}\)

D. \(x < -2\) or \(x > \frac{8}{3}\)

E. \(x \leq -2\) or \(x \geq \frac{8}{3}\)



When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know:
Rule #1: If |something| < k, then –k < something < k
Rule #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive


From rule #1, we can write: -7 < -3x + 1 < 7
Subtract 1 from all sides to get: -8 < -3x < 6
Divide all sides by -3 to get: 8/3 > x > -2 [since we divided by a NEGATIVE value, we had to REVERSE the inequality symbols]
Rewrite as: -2 < x < 8/3

Answer: B

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Re: If |-3x + 1| < 7, then which of the following represents all possible &nbs [#permalink] 31 Oct 2018, 06:08
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