Help with Inequalities Involving Absolute Value? Domain? Very confused! --- So m

Question

Help with Inequalities Involving Absolute Value? Domain? Very confused!
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So my Professor is going over it, and I'm very confused.

Please help explain how to do these/why that's the answer.
Solve the inequalities:
|x| < 1 Answer: -1 < x < 1

|x+2| < -10 Answer: 0 (I think that's what he put down)

|2x+1| > -5 Answer: All real #'s

|x-5| < 2 Answer: 3< x < 7

And I don't understand why the domain of x in ?5 - 2x Answer: 5 - 2x >/ (means more than or equal to) 0

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I'm having a real hard time, if you can explain these supposedly easy examples. This would totally help! Thanks!

Explanation / Answer

case 1:x+2=10 =>x=8 case2:x+2=-10 =>x=-12 so -12

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