Solve the following inequalities: |X+3| < 1Show step by step process to explain the solution and answer

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embizze eNotes educator| Certified Educator

Solve `|x+3|<1` :

First note that in an absolute value inequality, if you have `|a|<c` then your answer will be in a single range `-c<a<c` ; the absolute value indicates a distance. (If `|a|>c` then your answer has two parts; you can be far away in 2 directions e.g. `a>c` and `a<-c` )



Note that the value of the expression x+3 can take on any value from -1 to 1 (not inclusive) and satisfy the inequality.

`-4<x<-2`  ** subtract 3 from all parts of the inequality.


Thus your solution is the set of x's between -4 and -2, or