Chapter 4.9, Problem 14OE

To determine

To write the solution set of the inequality.

Answer to Problem 14OE

The solution set of the inequality is $\left\{x:x>3\text{ or }x<0\right\}$

Explanation of Solution

Given information:

The given inequality is $x\left(x-3\right)>0$

Calculation:

First write the inequality

  $x\left(x-3\right)>0$

The product is positive if and only if both factors have same sign.

Case 1: when both factors are positive.

  $\begin{array}{l}x>0\text{ and }\left(x-3\right)>0\\ x>3\left[\text{ add }\left(3\right)\text{to each side}\right]\end{array}$

The solution set of this conjunction is $\left\{x:x>3\right\}$

Case 2: when both factors are negative.

  $\begin{array}{l}x<0\text{ and }\left(x-3\right)<0\\ x<3\left[\text{ add }\left(3\right)\text{to each side}\right]\end{array}$

The solution set of this conjunction is $\left\{x:x<0\right\}$

Therefore,

The solution set of the inequality is $\left\{x:x>3\text{ or }x<0\right\}$