Quick Question, when would an inequality like this work: x^2 - 4x >or equal to 0?

Question

...What would I have to do to figure out when this would and would not work?

Answer 1

If you plot the graph, it will be a parabola concave up, with a zero at x=0, or x=4.
Therefore f(x)≤0 when x∈[0,4).
The correct answer would be
S={x|x∈(-∞,0]∪[4,+∞)}