Chapter 3.5, Problem 14AYU

$x^2\text{ + 7}x\text{ < }-\text{12}$

To determine

To find: The solution of the inequality $x^2+7x<-12$.

Answer to Problem 14AYU

Solution:

$-4<x<-3$

Explanation of Solution

Given:

The inequality is $x^2+7x<-12$

Calculation:

$x^2+7x+12<0$

$x^2+4x+3x+12<0$

$x\left(x+4\right)+3\left(x+4\right)<0$

$\left(x+4\right)\left(x+3\right)<0$

$\left(x+4\right)>0$ and $\left(x+3\right)<0$

$x>-4$ and $x<-3$

$-4<x<3$

Therefore the solution to the given inequality is $-4<x<3$.