Bell Quiz. Objectives Learn to graph inequalities. Write inequalities from a graph

Bell Quiz

Objectives

• Learn to graph inequalities. • Write inequalities from a graph.

Inequalities

• A liner inequality in one variable is an inequality that can be written as where and are real numbers.

• The solution of an inequality in one variable is a value or set of values that satisfies the inequality.

• To determine if a value is a solution to an inequality, substitute the value of the variable into the equation and simplify.– If the inequality statement is true, the value is part of

the solution set.

Example 1Identifying Solutions to Inequalities

Determine which of the values {0, 2, 4, 6,} are part of the solution set of the inequality.

Lesson Practice 1

Determine which of the values {– 2, 0, 5, 11 } are part of the solution set of the inequality.

Inequalities

• Equivalent inequalities are inequalities that have the same solution set.

• It is not always reasonable to list all the values in a solution set. Instead, a graph on a number line can represent the solution set of an inequality. – The graph shows the endpoint of the solution set as an open or closed

circle. – A heavy line and arrow indicate all values that are in the solution set.

Graphing Inequalities

• To create the graph of an inequality, first create a number line that includes the endpoint.

• Then determine if the endpoint should be shown with an open or closed circle.

• Finally, from the end point, draw a heavy line an arrowhead to show the solution.

Example 2Graphing Inequalities

Graph the inequality

Example 3Graphing Inequalities

Graph the inequality

Lesson Practice 2

Graph the inequality

Lesson Practice 3

Graph the inequality

Lesson Practice 4

Graph the inequality

Lesson Practice 5

Graph the inequality

Example 4Graphing Inequalities

Graph the inequality

Lesson Practice 6

Graph the inequality

Writing Inequalities

• The graph of an inequality can be translated to symbolic form.

• First identify the endpoint. – Is the endpoint is closed or open– Use or

Example 5Writing an Inequality from a Graph

Write the inequality of the graph.

Example 6Writing an Inequality from a Graph

Write the inequality of the graph.

Lesson Practice 7

Write the inequality of the graph.

Lesson Practice 8

Write the inequality of the graph.

Lesson Practice 9

Write the inequality of the graph.

Lesson Practice 10

Write the inequality of the graph.

Lesson Practice 11

Write the inequality of the graph.

Lesson Practice 12

Write the inequality of the graph.

Example 7Application: Practice Time

Marie does not take a break until she has practiced playing the violin for at least half an hour. a. Write an inequality to represent the number of

hours that Marie must practice before she takes a break.

b. Graph the solution set of the inequality.

Lesson Practice 13