Help with Inequalities Involving Absolute Value Domain Very

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!

|x|<1 Let\'s consider: |x|=1... x=-1,1 because |-1|=1 and |1|=1 <-------0-------|-------0-------> -1 0 1 Any x greater than -1 and less than 1 will satisfy... |x|<1 Do you agree? Therefore, -1 -5 Answer: All real #\'s YES Let\'s say 2x+1 = 10; then |2x+1|=10 and 10>-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< x < 7 Consider |x-5| = 2 This means x-5 = 2 and x-5 = -2. Solve both equations... x-5 = 2 x-5+5 = 2+5 x=7 x-5 = -2 x-5+5 = -2+5 x=3 <-------0--------------0-------> 3 7 Let\'s return to |x-5| < 2 If x is less than 3, does x satisfy |x-5| < 2 ? NO If x is greater than 7, does x satisfy |x-5| < 2 ? NO But, if x is greater than 3 and less than 7, pick any three numbers between 3 and 7, does x satisfy |x-5| < 2 ? YES... Therefore, the solution of |x-5| < 2 is 3

$Help with Inequalities Involving Absolute Value? Domain? Very confused!. --- So my Professor is going over it, and I\'m very confused. Please help explain how t$

Help with Inequalities Involving Absolute Value Domain Very

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