How $x^2 + 5x + 6 \ge 0$ implies $−3 \ge x \ge −2$ ?
I represented $x^2 + 5x + 6 \ge 0$ as $(x+3)(x+2) \ge 0$,which means that either $(x+3) \ge 0$ and $(x+5) \ge 0$ which giving $x \ge -3$ or $x \ge -2$ but how does this gives $−3 \ge x \ge −2$?
ADDED: The above expression could also mean that $(x+3) \le 0$ and $(x+2) \le 0$ which will give $x \le -3$ and $x \le -2$,now should combine this two to get that result? but in that case we would get both $−3 \le x \le −2$ and $−2 \le x \le −3$ (if I am not wrong) but then the first one should be takes as the answer is taken as the second one makes no sense,am I right?
Source of the problem. Check the solution given there which causes the confusion.