Question 9334
4x^2 - 8x >= 0

 Factor left side

 4x(x - 2) >=0

 Then case I) 4x <=0 and x - 2 <= 0

  so x <= 0 and x <= 2

 So x <= 0

 This is graphed on a number line by putting a solid dot at 0 and an arrow pointing to the left of point 0

 case II) 4x >= 0 and x-2 >= 0

 so x >= 0 and x >= 2

 So x >= 2

 The solution of 4x^2 - 8x >= 0 is x<= 0 or x>= 2
Interval notation of solution: (-infinity,0] or [2,infinity)
 We graphed the first part of the solution
The second is graphed by putting a solid dot at point 2 on a number line and drawing an arrow to the right of this point

To solve 3x - x^2 > 0 

 factor left side

 x(3 - x) > 0

 Then case i) x < 0 and 3 - x < 0

  x< 0 and 3 < x

 This is false

 so case ii) x > 0 and 3 - x > 0

 x > 0 and 3 > x

 0 < x < 3
Interval notation is (0,3)
 To graph this solution, put open dots at points 0 and 3 on a number line
and draw a line segment between them.