Question 119470
<pre><font size = 6 face = "book antiqua" color = "darkblue"><b>
|2x| < x+5

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

Then |2x| = 2x and

x <u>></u> 0 and 2x < x + 5

x <u>></u> 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</pre>