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