## Precalculus (6th Edition) Blitzer

The value of the expression $6{{x}^{2}}-6<5x$ is $\left( -\frac{2}{3},\frac{3}{2} \right)$.
Rearrange the following expression as given below: \begin{align} & 6{{x}^{2}}-6<5x \\ & 6{{x}^{2}}-6-5x<0 \\ & 6{{x}^{2}}-5x-6<0 \\ & 6{{x}^{2}}-9x+4x-6<0 \end{align} And simplify it further to get: \begin{align} & 3x\left( 2x-3 \right)+2\left( 2x-3 \right)<0 \\ & \left( 2x-3 \right)\left( 3x+2 \right)<0 \end{align} Again, solve the inequality $\left( 2x-3 \right)\left( 3x+2 \right)<0$ as given below: $\left( 2x-3 \right)<0$ And $\left( 3x+2 \right)>0$ Or: $\left( 2x-3 \right)>0$ And $\left( 3x+2 \right)<0$ Then, from the first condition we get $x-\frac{2}{3}$. From the second condition we get $x>\frac{3}{2}$ and $x-\frac{2}{3}$ and \$ x