Chapter 3.5, Problem 15AYU

$2x^2\text{ < 5}x\text{ + 3}$

To determine

To find: The solution of the inequality $2x^2<5x+3$.

Answer to Problem 15AYU

Solution:

$-\frac{1}{2}<x<3$

Explanation of Solution

Given:

The inequality is $2x^2<5x+3$

Calculation:

$2x^2-5x-3<0$

$2x^2-6x+x-3<0$

$2x\left(x-3\right)+1\left(x-3\right)<0$

$\left(x-3\right)\left(2x+1\right)<0$

$\left(x-3\right)<0$ and $\left(2x+1\right)>0$

$x<3$ and $x>-\frac{1}{2}$

$-\frac{1}{2}<x<3$

Therefore the solution to the given inequality is $-\frac{1}{2}<x<3$.