How to Solve Modulus for x+2: -5<x<1

[essaichay]

Hi everyone,

Ok I'm trying to revise modulus functions etc and this is supposed to be an 'easy' question but I came up with the wrong answer so now I'm getting confused.

I have to solve |x+2| - 1 <2

I used the formula: |x| < b <------> -b < x < b

And this is how I used it:

|x + 2| - 1<2
|x + 2|<3
-3< x + 2 <3
-1< x <5

Which is supposedly wrong because in the answer booklet it gives the solution: -5< x<1

AHH I'm so confused, sorry. I don't know if there's supposed to be another formula or something. My teacher taught us the squaring way but to be honest, in exams that just provides me with loads of working out to do which is tiring.

Thanks in advance to anyone who can help me on this!

 

[Vid]

You added 2 instead of subtracting in the last step.

 

[essaichay]

You added 2 instead of subtracting in the last step.

LOOOOOOOLLLL omg. THANK YOU. I have truly kicked myself.

 

[essaichay]

Also, how would ou go about solving this inequality:S?:

|x+2| <3|x|

I don't know if you can apply the rule I used before again to this question.

Thanks.

 

[HallsofIvy]

Break it into 3 parts: x< -2, $-2\le x < 0$, and $0\le x$.