Last visit was: 27 Apr 2026, 01:21 It is currently 27 Apr 2026, 01:21
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
tamalmallick
User avatar
Joined: 16 Apr 2019
Last visit: 29 Jan 2023
Posts: 8
Own Kudos:
3
Given Kudos: 5
Posts: 8
Kudos: 3
Problem solving Inequality absolute value 05 Jun 2019, 00:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
While solving absolute inequality questions, I have gone through 1 question and found the following solution.

The question was

What is the solution of the following equation 7 > |-3a + 5|,

Solution was
i.
7 > +(-3a+ 5)
2 > -3a
2/3>-a
a>-2/3

and
ii.
7 > -(-3a + 5)
7 > 3a
12 > 3a
4 > a

so the solution is
-2/3<a<4

If the above-mentioned solution is correct, then it is diluting the meaning of the absolute value of "-3a + 5". Why we are considering both +ve and -Ve values of -3a + 5, when only abolute value is less than 7. The negative value of "-3a + 5" may not be lesser than 7. Then how can we consider negative value as one of the solutions.

If anybody can explain the logic behind this, please comment.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
ccooley
User avatar
Manhattan Prep Instructor
Joined: 04 Dec 2015
Last visit: 06 Jun 2020
Posts: 931
Own Kudos:
1,658
Given Kudos: 115
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Posts: 931
Kudos: 1,658
Problem solving Inequality absolute value 10 Jun 2019, 14:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
tamalmallick
While solving absolute inequality questions, I have gone through 1 question and found the following solution.

The question was

What is the solution of the following equation 7 > |-3a + 5|,

Solution was
i.
7 > +(-3a+ 5)
2 > -3a
2/3>-a
a>-2/3

and
ii.
7 > -(-3a + 5)
7 > 3a
12 > 3a
4 > a

so the solution is
-2/3<a<4

If the above-mentioned solution is correct, then it is diluting the meaning of the absolute value of "-3a + 5". Why we are considering both +ve and -Ve values of -3a + 5, when only abolute value is less than 7. The negative value of "-3a + 5" may not be lesser than 7. Then how can we consider negative value as one of the solutions.

If anybody can explain the logic behind this, please comment.
Show more

First of all, the solution is correct. A good way to double check that it's correct is to plug in some values for a. The solution says that a is between -2/3 and 4; try the extreme values:

|-3(-2/3) + 5| = |2 + 5| = |7| = 7, so if a is a tiny bit greater than -2/3 (closer to 0), the absolute value will be less than 7.

|-3(4) + 5| = |-12 + 5| = |-7| = 7; likewise.

Also, try at least one value in the middle:

|-3(0) + 5| = |5| = 5, which is less than 7.

It seems like the answer is right.

I'm not totally sure I understand your question, but I think your concern has something to do with the idea of the 'negative value' of -3a + 5. Be aware that the 'negative value' of this expression isn't necessarily a negative number. For example, if a = 3, then the 'negative value' is -(-3a + 5) = -(-4) = 4. Think of the negative sign as being a 'reverse the sign' marker, not a marker saying that the expression has to be negative.

Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!