For the first inequality you are almost right, but let's distinguish < and <=. The correct answer is not "-1,3" but (-1, 3] (3 is suitable, -1 is not).

For the second... there is no answer and I afraid you made a mistake when multipluing inequality by -1. In such a case sign of inequality changes. Let's solve from the beginning:

2x+3<-1 OR 10-x<5,

2x<-4 OR -x<-5,

x<-2 OR x>5.

So all x that less than -2 suit us, all x that greater than 5 also suit us: (-infinity; -2) and also (5; +infinity).

In a set theory this is called union and denoted as U:

(-infinity; -2) U (5; +infinity) is the answer.

Apr 7th, 2015

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