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HELP! No idea how to do this...?
The questions are:
Solve these inequalities:
a) (2x-5) / (x+1) < 1
b) (2x-7) / (x+5) > 4
I have no idea how you would approach these. I would be very grateful if someone could help me and explain fully how they got the answer.
1 Answer
- 9 years agoFavorite Answer
a) (2x-5) / (x+1) < 1
We want to simplify this by multiplying both sides by (x+1). However, if (x+1) is negative, this will change the direction of the inequality, so we have to take the cases x>-1 and x<-1 separately.
If x>-1, x+1 is positive:
2x-5 < x+1, so x-5 < 1, so x < 6.
So inequality a) is true for -1 < x < 6.
If x<-1, x+1 is negative:
2x-5 > x+1, so x > 6.
But x<-1 and x>6 contradict each other, so there are no values of x<-1 satisfying inequality a).
Final answer: -1 < x < 6.
b) is very similar; you have to take the cases x>-5 and x<-5 separately. The answer you end up with is -6.5 < x < -5.
