SOLUTION: |2x| < x+5

Algebra ->  Absolute-value -> SOLUTION: |2x| < x+5       Log On


   

Question 119470: |2x| < x+5
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!

|2x| < x+5

Case 1: x > 0 and |2x| < x+5

Then |2x| = 2x and

x > 0 and 2x < x + 5

x > 0 and x < 5

 [0, 5)

Case 2: x < 0 and |2x| < x+5

Then |2x| = -2x and

x < 0 and -2x < x + 5

x < 0 and -3x < 5

x < 0 and x > -5/3

(-5/3, 0)

So solution is

Case 2 U Case 1

(-5/3, 0) U [0, 5)

or 

(-5/3, 5) 

Edwin