GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Nov 2018, 06:09

# LBS is Calling R1 Admits - Join Chat Room to Catch the Latest Action

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

November 22, 2018

November 22, 2018

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
• ### Key Strategies to Master GMAT SC

November 24, 2018

November 24, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50729
If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

### Show Tags

13 Jul 2018, 00:01
00:00

Difficulty:

15% (low)

Question Stats:

72% (01:07) correct 28% (01:05) wrong based on 279 sessions

### HideShow timer Statistics

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 $$x \geq \frac{8}{3}$$

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7044
Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

### Show Tags

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
_________________

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

GMAT online Tutor

Math Expert
Joined: 02 Sep 2009
Posts: 50729
Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

### Show Tags

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.
_________________
Director
Joined: 31 Oct 2013
Posts: 797
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

### Show Tags

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 .

Manager
Joined: 24 Jan 2015
Posts: 55
Location: India
If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

### Show Tags

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
Math Expert
Joined: 02 Aug 2009
Posts: 7044
Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

### Show Tags

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

GMAT online Tutor

Director
Joined: 31 Oct 2013
Posts: 797
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If |–3x + 1| < 7, then which of the following represents all possible  [#permalink]

### Show Tags

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

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8580
Location: Pune, India
If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

### Show Tags

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

For more, check:
https://www.veritasprep.com/blog/2011/0 ... edore-did/
_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

CEO
Joined: 11 Sep 2015
Posts: 3130
Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

### Show Tags

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

RELATED VIDEO

_________________

Test confidently with gmatprepnow.com

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