Chapter 3.6, Problem 8LC

To determine

Comparing the graph of compound inequalities containing “ and” and “ or”.

Answer to Problem 8LC

In “or” statement can include both equation terms and in “and” statement the numbers come which are in common on graph.

Explanation of Solution

When the inequality containing “or”

For example:

  $\begin{array}{l}h+3>12\text{ or 3-2h}>\text{9}\\ \text{h}>\text{9 or h}<\text{-3}\end{array}$

So the graph for this equation will be:

  

The compound inequality is  or  statement, it includes all numbers in each solutions, which in this case is all numbers on number line.It will represent as $\text{h}>\text{9 or h}<\text{-3}$

When the inequality containing “and”

For example :

  $\text{-8 }\le \text{x and x < -1}$

So the graph for this equation will be:

  

 In this case, you can rewrite $\text{-8 }\le \text{x and x < -1}$   as $-8\le x<-1$ since the solution is between -8 and -1, including -8 In “or” statement can include both equation terms and in “and” statement the numbers come which are in common on graph.