solve the compound inequality. write the solution in interval notation

Question

-3<2x+1<=3

Answer 1

Treat both < signs as equals signs so  instead of just subtract 1 from 2 sides you must do it three times.

 

-3 < 2x +1 <= 3  ---->    -3 - 1 < 2x +1 - 1 <= 3 - 1     which becomes   -4< 2x <= 2

 

divide by 2 in all three zones.   -4/2 < 2x/2 < 2/2 which becomes  -2 < x <= 1 so our answer is between -2 and 1 including 1. 

 

Interval notation:  (-2, 1]