>>1074565If the equation does have solutions, those solutions are points where the
See pic related. This is x^2 - x + 1 and the line y = 10. We find the solutions to the equation, it looks like they're about -2.5, and 3.5
If we're looking at the inequality x^2 - x + 1 < 10, every value between -2.5 and 3.5 is a solution.
If we're looking at the inequality x^2 - x + 1 > 10, every value outside of -2.5 and 3.5 is a solution.
So to find out which, all we need to do is plug in a value, any value, between the two solutions. Again, 0 is a good choice here. If this leads to a true inequality, that means every x between the two solutions to the equation is a solution to the inequality. If this leads to a false inequality, that means that every x outside the two solutions to the equation is a solution to the inequality.
Does that make sense?
