Chapter 3.5, Problem 7AYU

$x^2-\text{ 3}x-\text{ 10 < 0}$

To determine

To find: The solution of the inequality $x^2-3x-10<0$.

Answer to Problem 7AYU

Solution:

$-2<x<5$

Explanation of Solution

Given:

The inequality is $x^2-3x-10<0$.

Calculation:

$x^2-3x-10<0$

$x^2-5x+2x-10<0$

$x\left(x-5\right)+2\left(x-5\right)<0$

$\left(x-5\right)\left(x+2\right)<0$

$\left(x-5\right)<0$ and $\left(x+2\right)>0$

$x<5$and $x>-2$

Therefore the solution to the given inequality is $-2<x<5$.