Rational inequality

Question

x²+18<5x

Please help me solve this. I can usually solve these but can't figure this one out.

Thanks!

Answer 1

Put all of the terms on one side, giving a quadratic expression that must be < 0.

 

x² -5x +18 < 0; can't be factored. However, the left side represents a parabola and you can find its zeros, using the quadratic formula. But wait! The discriminant is 25 - 4(1)(18), which is negative, therefore there are no zeros (x-intercepts) and since this parabola opens upward and its vertex is above the x-axis, the quadratic expression is never zero or negative.  Therefore there is NO SOLUTION.