Chapter 8.6, Problem 44HP

To determine

Explain how to tell the difference between graphing an inequality with a closed circle and one with open circle. Use example to clarify you explanation.

Answer to Problem 44HP

A closed, or shaded, circle is used to represent the inequalities greater than or equal to ( $\ge$ ) or less than or equal to ( $\le$ ). The point is part of the solution.

An open circle is used for greater than (>) or less than (<). The point is not part of the solution. The graph then extends endlessly in one direction.

Explanation of Solution

Given:

Explain how to tell the difference between graphing an inequality with a closed circle and one with open circle. Use example to clarify you explanation.

Concept Used:

Difference between the meanings closed circle and open circle on the number line:

A closed, or shaded, circle is used to represent the inequalities greater than or equal to ( $\ge$ ) or less than or equal to ( $\le$ ). The point is part of the solution.

An open circle is used for greater than (>) or less than (<). The point is not part of the solution. The graph then extends endlessly in one direction.

Example for open circle:

An open circle is used for greater than (>) or less than (<). The point is not part of the solution. The graph then extends endlessly in one direction

  $p<14$

  

  $p>14$

  

A closed, or shaded, circle is used to represent the inequalities greater than or equal to ( $\ge$ ) or less than or equal to ( $\le$ ). The point is part of the solution.

  $p\le 14$

  

  $p\ge 14$