Chapter 4.9, Problem 5WE

To determine

To find and graph: The given equation of each inequality.

Answer to Problem 5WE

The solution set of the given inequality is,

  $\left\{x:z\ge 4\text{ or z}\ge 0\right\}$

Explanation of Solution

Given information: The equation is given as: $z^2-4z>0$

Calculation:

The solution set of the given equation can be find as:

  $\begin{array}{l}{z}^2-4z>0\text{ write original eqaution}\text{.}\\ z\left(z-4\right)\text{>0 factor the polynomial}\text{.}\end{array}$

To draw a sign graph, draw a number line for each and label the part where the factor is positive, where it is zero and where it is negative.

The graph can be obtained as:

  

The sign of the product $z\left(z-4\right)\text{>0}$ is determined by the number of negative factors. When exactly one or exactly three factors are negative, the product is negative. When no factors or exactly 2 factors are negative, the product is positive.

  

The solution set of the given inequality is,

  $\left\{x:z\ge 4\text{ or z}\ge 0\right\}$