# How do you solve  10 + x - 2x^2 <0? c) -2 + 7x - 3x^2<0

Jan 21, 2016

graph{2x^2-x-10 [-10, 10, -5, 5]} 2x-5)(x+2)<0 # Thus per the inequality the true set include only
The left hand side of the quadratic less that zero, i.e. -2

#### Explanation:

Multiply the entire equation by -1 and find it factors (true set):
$10 + x - 2 {x}^{2} = 2 {x}^{2} - x - 10 < 0$
$\left(2 x - 5\right) \left(x + 2\right) < 0$ Thus per the inequality the true set include only
The left hand side of the quadratic less that zero, i.e. -2
look at the graph for clarity.
you should try the 2nd problem yourself usin the same approach and rational I provided you here