|2x-5|/|2x-1|<1/2 I need you to list solution in interval notation pls. Tnx


We get 0 on the right by subtracting 2 from both sides:



We first find the endpoints by solving the equation:



Which involves solving two equations:

 and  

The first gives solution  and the second gives
solution 11/6

 is about 4.5 and {{11/6}}} is about 1.8333···

Mark those on a number line:

-------------------------o---------------o---------
-2     -1     0     1     2     3     4     5     6 

Test a value to the left of . The easiest
value is 0.  Substitute it into the original
inequality:







That is clearly false so do not shade the part to the
left of .  So we still have just:

-------------------------o---------------o---------
-2     -1     0     1     2     3     4     5     6 

Now test a value between  and .
The easiest value is 2.  Substitute it into the original
inequality:







That is true so we do shade the part between
 and .  Now we have this:

-------------------------o===============o---------
-2     -1     0     1     2     3     4     5     6

Now we test a value to the right of . The easiest
value is 5.  Substitute it into the original
inequality:







That is clearly false so do not shade the part to the
rightt of .

So the graph of the solution is

-------------------------o===============o---------
-2     -1     0     1     2     3     4     5     6

and the interval notation is



Edwin