Chapter 4.4, Problem 49AYU

To determine

To calculate:

The following inequality equation:

  $\left(x+1\right)\left(x-3\right)\left(x-5\right)>0$

Answer to Problem 49AYU

The solution of the inequality equation $\left(x+1\right)\left(x-3\right)\left(x-5\right)>0$ is $x=3,5$ .

Explanation of Solution

Given information:

  $\left(x+1\right)\left(x-3\right)\left(x-5\right)>0$

Calculation:

The given equation is:

  $\begin{array}{l}\left(x+1\right)\left(x-3\right)\left(x-5\right)>0\\ x+1=0OR\text{}x-3=0OR\text{}x-5=0\\ x=-1x=3x=5\end{array}$

The inequality value should be greater than zero, from the above solution $-1<x<3,x>5$ .

Hence, the inequality is solved for $x<0,\left(3,5<0\right)$ .