victorywillbemine wrote:

Hi,

My first post on GMAT Club.I have just kick started my prep for GMAT, get always stuck at the inequalities. Need a bit of help.

Q. x^2+8x+7<0

solution is -7<x<-1

i can break down the equation to (x+1)(x+7)<0

post this x+1<0 the x<-1 which is true as per the answer

but if i follow the similar process for x+7<0 the x<-7 which is not true as per the answer.

please clear my basic, when "<" sign is there in question does the inequality equation follow certain rules.

one more similar question

Q x^2+7x+12>0

answer: x<-4 and x>-3

according to me it should be x>-3 and x>-4 hence solution should be x>-4 .................

its confusing

.............please help!!!!!!

Welcome to GMAT club.

The rule is once u get the solution you need to ascertain its validity or you need to plug in that solution back in equation and test for validity. for example:

for first equation, once you've reached to (x+1)(x+7)<0

Now you know that for this to be true, one term must be negative and other positive.

say (x+1) is negative => x <-1

but at this time x+7 must be positive, so x+7 > 0 => x>-7

Hence we get the range -7 <x<-1

Again second possibility,

if x+1 is positive then x+7 should be negative or

x+1 >0 => x >-1

and x+7 <0 => x < -7

but it is not possible. Since x can not be greater than -1 and less than -7 at same time.

So you get that the solution obtained first was correct one. and range is -7<x<-1

similarly you can solve the second problem.

Once you are comfortble getting ans like this, then slowly u can move to graphical approach which makes it even easier to get the answer by knowing the concept.

Hope it helps.

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