Chapter 3.5, Problem 21AYU

$6\left(x^2-\text{ 1}\right)\text{ > 5}x$

To determine

To find: The solution of the inequality $6\left(x^2-1\right)>5x$.

Answer to Problem 21AYU

Solution:

$x>\frac{3}{2}$ or $x<-\frac{2}{3}$

Explanation of Solution

Given:

The inequality is $6\left(x^2-1\right)>5x$

Calculation:

$6\left(x^2-1\right)>5x$

$6x^2-6-5x>0$

$6x^2-5x-6>0$

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

$3x\left(2x-3\right)+2\left(2x-3\right)>0$

$\left(2x-3\right)\left(3x+2\right)>0$

$\left(2x-3\right)>0$ or $\left(3x+2\right)<0$

$x>\frac{3}{2}$ or $x<-\frac{2}{3}$

Therefore the solution is $x>\frac{3}{2}$ or $x<-\frac{2}{3}$.