Chapter 3.5, Problem 22AYU

$2\left(2x^2-\text{ 3}x\right)\text{ > }-\text{9}$

To determine

To find: The solution of the inequality $2\left(2x^2-3x\right)>-9$.

Answer to Problem 22AYU

Solution:

No real solutions

Explanation of Solution

Given:

The inequality is $2\left(2x^2-3x\right)>-9$

Calculation:

$2\left(2x^2-3x\right)>-9$

$4x^2-6x+9>0$

The discriminant value of the above inequality is:

$b^2-4ac={\left(-6\right)}^2-4\left(4\right)\left(9\right)=36-144=-108<0$

Therefore the given inequality has no real solutions.