SOLUTION: Please help me solve the following question: Solve and write in interval notation for the solution set: The absolute value of x+2 greater than or equal to 4

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Question 163007: Please help me solve the following question:
Solve and write in interval notation for the solution set:
The absolute value of x+2 greater than or equal to 4

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve the following question:
Solve and write in interval notation for the solution set:
The absolute value of x+2 greater than or equal to 4 

abs%28x%2B2%29%3E=4

The rules for removing the absolute value bars in inequalities
are

1. abs%28EXPRESSION%29%3CA can be rewritten as -A%3CEXPRESSION%3CA

2. abs%28EXPRESSION%29%3C=A can be rewritten as -A%3C=EXPRESSION%3C=A

3. abs%28EXPRESSION%29%3EA can be rewritten as EXPRESSION%3C-A_OR_EXPRESSION%3EA

4. abs%28EXPRESSION%29%3E=A can be rewritten as EXPRESSION%3C=-A_OR_EXPRESSION%3E=A

Your problem:
abs%28x%2B2%29%3E=4

is case 4.

abs%28x%2B2%29%3E=4 

can be rewritten as

x%2B2%3C=-4_OR_x%2B2%3E=4

Add -2 to both sides in both parts:

x%2B2-2%3C=-4-2_OR_x%2B2-2%3E4-2

      x%3C=-6_OR_x%3E2

<==========@-----------------------@=========>
 -9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5

   

Edwin