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

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

|x|-5 Let's say 2x+1 = -10; then |2x+1|=|-10|=10 and 10>-5 Let's say 2x+1 = 0; then |2x+1|=|0|=0 and 0>-5 Like we saw before... 2x+1 can be zero or any positive or negative number, |2x+1| will ALWAY be zero or a positive number and zero and EVERY positive number is greater than -5. Therefore, 2x+1 can be any real number and so x can be any real number. Prove this for yourself... calculate |2x+1| when x= -10, -9, -8, ..., 0, ..., 8, 9, 10. |x-5| < 2 Answer: 3

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