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

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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13 Jul 2018, 00:01
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00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:30) correct 24% (01:34) wrong based on 333 sessions

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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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Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Math Expert
Joined: 02 Sep 2009
Posts: 52971
Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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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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VP
Joined: 31 Oct 2013
Posts: 1136
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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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: 53
Location: India
If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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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: 7334
Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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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
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

VP
Joined: 31 Oct 2013
Posts: 1136
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: If |–3x + 1| < 7, then which of the following represents all possible  [#permalink]

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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: 8883
Location: Pune, India
If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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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/
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Karishma
Veritas Prep GMAT Instructor

CEO
Joined: 11 Sep 2015
Posts: 3435
Re: If |-3x + 1| < 7, then which of the following represents all possible  [#permalink]

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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

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