Target Test Prep's 2024 GMAT Focus Edition prep is discounted for the BTG community!

Redeem
Target Test Prep
5-Day Free Trial
5-day free, full-access trial TTP

Available with Beat the GMAT members only code

MORE DETAILS
Target Test Prep
Magoosh
Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

MORE DETAILS
Magoosh

Not a question but an intermediary step

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Mon Oct 05, 2015 10:32 am

Not a question but an intermediary step

by sushantsahaji » Mon Apr 25, 2016 7:40 pm
Is |2x+5|>= -3 a valid statement?

It is mentioned in one of the questions answer.
If valid, why? Can |2x+5| be equal to -3?

Regards,

Sushant
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 410
Joined: Fri Mar 13, 2015 3:36 am
Location: Worldwide
Thanked: 120 times
Followed by:8 members
GMAT Score:770

by OptimusPrep » Mon Apr 25, 2016 7:58 pm
sushantsahaji wrote:Is |2x+5|>= -3 a valid statement?

It is mentioned in one of the questions answer.
If valid, why? Can |2x+5| be equal to -3?

Regards,

Sushant
I am having difficulty in understanding your question. I would be better if you posted the entire question, but let me try.

Case 1:
x >= - 5/2 - (i)
In this case, modulus will open with a positive sign.
2x + 5 >= -3
2x >= -8
x >= -4 (ii)
From (i) and (ii), x >= -5/2

Case 2:
x < -5/2 - (iii)
In this case, modulus will open with a negative sign.
2x + 5 < -3
2x < -8
x < -4 - (iv)
From (iii) and (iv), x < -4
Top
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Mon Oct 05, 2015 10:32 am

by sushantsahaji » Tue Apr 26, 2016 2:34 am
Hi,

Solve |2x+5|+4>=1 is the original question. Question is not tough to solve. But I have a doubt in second step,

|2x+5|>=-3. (|2x+5|can never be equal to -3.)

So, is the above statement valid?
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Tue Apr 26, 2016 4:13 am
sushantsahaji wrote:Hi,

Solve |2x+5|+4≥1 is the original question.
Strange problem.
Since an absolute value cannot be negative, |2x+5| ≥ 0.
Thus, the least possible value of |2x+5| + 4 is 4.
Since |2x+5| + 4 ≥ 4, it is not possible that |2x+5| + 4 = 1.
That said, any value of x will satisfy the inequality in red.

I would ignore this problem.
What is the source?
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Mon Oct 05, 2015 10:32 am

by sushantsahaji » Wed Apr 27, 2016 3:23 am
Thank you Mitch.
Source of the problem: https://www.regentsprep.org/regents/math ... actice.htm
Practice website suggested on Gmatprepnow.
GMATGuruNY wrote:
sushantsahaji wrote:Hi,

Solve |2x+5|+4≥1 is the original question.
Strange problem.
Since an absolute value cannot be negative, |2x+5| ≥ 0.
Thus, the least possible value of |2x+5| + 4 is 4.
Since |2x+5| + 4 ≥ 4, it is not possible that |2x+5| + 4 = 1.
That said, any value of x will satisfy the inequality in red.

I would ignore this problem.
What is the source?
Top
Post new topic Post Reply
• Page 1 of 1