Inequality Problem

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pm; Thanked: 114 times; Followed by:11 members

Inequality Problem

by knight247 » Mon Aug 22, 2011 11:36 am

Find the range of values of x for which xÂ²+7x+12>0
(A)-4<x<-3
(B)x<-4 or x>-3
(C)x<-4 and x>-3
(D)x<3 or x>4
(E)3<x<4

OA is B

I solved the eqn like a regular quadratic equation until I reach (x+3)(x+4)>0
At which point I figure that either both terms are +ve or both are -ve
x>-3 and x>-4
or
x<-3 and x<-4

I really don't know how to choose the correct extremities from the answers I get. Hope someone can give me a detailed explanation. Thanks

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Source: Beat The GMAT — Problem Solving | Mon Aug 22, 2011 11:36 am

sumgb: Senior | Next Rank: 100 Posts; Posts: 64; Joined: Sun Jul 24, 2011 9:11 am; Thanked: 13 times; GMAT Score:610

by sumgb » Mon Aug 22, 2011 1:24 pm

you have almost solved the problem

I solved the eqn like a regular quadratic equation until I reach (x+3)(x+4)>0
At which point I figure that either both terms are +ve or both are -ve

as you know +ve * +ve = +ve or -ve * -ve = +ve
so both (x+3) and (x+4) should have same sign (either +ve or -ve)
case I: when both are -ve; x must be less than -4 so that both (x+3) and (x+4) are -ve; hence x <-4
case II:when both are +ve; x must be greater than -3 so that both (x+3) and (x+4) are +ve; hence x >-3

Ans B

hope this helps..

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Whitney Garner: GMAT Instructor; Posts: 273; Joined: Tue Sep 21, 2010 5:37 am; Location: Durham, NC; Thanked: 154 times; Followed by:74 members; GMAT Score:770

by Whitney Garner » Mon Aug 22, 2011 2:47 pm

knight247 wrote:Find the range of values of x for which xÂ²+7x+12>0
(A)-4<x<-3
(B)x<-4 or x>-3
(C)x<-4 and x>-3
(D)x<3 or x>4
(E)3<x<4

OA is B

I solved the eqn like a regular quadratic equation until I reach (x+3)(x+4)>0
At which point I figure that either both terms are +ve or both are -ve
x>-3 and x>-4
or
x<-3 and x<-4

I really don't know how to choose the correct extremities from the answers I get. Hope someone can give me a detailed explanation. Thanks

You've done everything perfectly so far! Now you just need to condense each of your inequalities.

For the first, x>-3 and x>-4, you need to write one inequality that represents where BOTH of those are true - so you're basically looking for the most restrictive. In this case, if x is a number bigger than -3, then it will take care of BOTH restrictions that x be bigger than -3 AND bigger than -4. So we can write x>-3.

For the second, x<-3 and x<-4, we again need to find the most restrictive inequality. If x is a number smaller than -3, it DOES NOT ensure that x is also less than -4. BUT, if we go with the alternative and say that x is less than -4, then it does cover the restriction that x also be less than -3. So we can write x<-4.

And now we have the 2 sides of the inequality - the expression will be true whenever x>-3 or when x<-4.

Hope this helps!

whit

Whitney Garner
GMAT/GRE/EA Instructor & Anxiety/Accommodations Coach
www.whitneygarner.com

Contributor to Beat The GMAT!

Math is a lot like love - a simple idea that can easily get complicated