I've attached an example. You can use the table method for the polynomial inequalities too. First factor them and find the critical points. Hope this helps.
Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation.
x-2/x+1 <0
my answer: (-infinity,-1) u (2, infinity)
-x+8/x-3 > or equal to 0
my answer: (3,8]
2/x-2<1
my answer: (2,4)
10-2x/4x+5 < or equal to 0
my answer: (-infinity, -5/4) or [5, infinity)
Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation.
x^2 - 6x + 5 > 0
-I got (-ininity,1) u (5, infinity)
x^2 - 3x - 18 < 0
-I got (-infinity,-3) u (6, infinity)
x^2 - 3x - 28 ¡Ü 0
-I got (-ininity,-4] u [7,infinity)