Chapter 3.5, Problem 16AYU

$6x^2\text{ < 6 + 5}x$

To determine

To find: The solution of the inequality $6x^2<6+5x$.

Answer to Problem 16AYU

Solution:

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

Explanation of Solution

Given:

The inequality is $6x^2<6+5x$

Calculation:

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

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

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

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

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

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

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

Therefore the solution to the given inequality is $-\frac{2}{3}<x<\frac{3}{2}$.