How do I solve for x: | x + 2 | >= 3/2? ?

Question

How do I solve for x: | x + 2 | >= 3/2? ?

Answer 1

|x + 2| >= 3/2

x + 2 >= +/- 3/2

x = 3/2 - 2

x = 3/2 - 4/2

x = -1/2

...AND...

x = -3/2 - 2

x = -3/2 - 4/2

x = -7/2

Answer 2

The answer the zhengfoo provided is not entirely correct.

Since you are dealing with absolute value, you have two cases:

Case 1: Positive absolute value

x + 2 >= 3/2

x >= 3/2 - 2

x >= -1/2

Case 2: Negative absolute value

-(x + 2) >= 3/2

-x - 2 >= 3/2

-x >= 3/2 + 2

-x >= 7/2

x <= -7/2

So, from case 1 you have x >= -1/2 and from case 2 you have x <= -7/2.

Therefore, the solution is (-∞,-7/2] U [-1/2,∞) <---- this is how you should write your solution.