z^2 - 4z > 0 Give solution set (Graphing on # line)?

Question

Please show the steps too. Im get it to z (z-4) > 0 then idk what to do please help

Answer 1

For z(z-4) to be positive, z and z-4 must have the same sign. Therefore, either:
1) z>0 and z-4>0, so z>4
2) z<0 and z-4<0, so z<0.
Therefore, the solution set is { z | z > 4 or z < 0 }

Answer 2

find the critical points. Those occur when the expression on the left is equal to 0
so those points are 0 and 4
those points divide the number line into 3 parts: <0, 04

Choose test numbers for each section and plug then into the original equation to see which sections fit the inequality

Answer 3

Factor it.

z(z - 4) > 0 only when z and z - 4 are both negative or when they are both positive. If z < 0, z - 4 is also negative, so z < 0 works. If z - 4 > 0, then z is also positive. So z > 4 works.

The solution set is (-inf, 0) U (4, inf).