|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
