Answer
The value of the expression $6{{x}^{2}}-6<5x $ is $\left( -\frac{2}{3},\frac{3}{2} \right)$.
Work Step by Step
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
