3 1 Graphing and Writing Inequalities Objectives Identify

3 -1 Graphing and Writing Inequalities Objectives Identify solutions of inequalities with one variable. Write and graph inequalities with one variable. Holt Algebra 1

3 -1 Graphing and Writing Inequalities An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs: ≥ ≠ A≤B A≥B A≠B A is less than or equal to B. A is greater than or equal to B. A is not equal to B. < > ≤ A<B A>B A is less than B. A is greater than B. A solution of an inequality is any value that makes the inequality true. Holt Algebra 1

3 -1 Graphing and Writing Inequalities Graphing Inequalities Dot Line ≤ or ≥ : Solid dot > or ≥ : Draw line on right < or > : Open dot < or ≤ : Draw line on left Holt Algebra 1

3 -1 Graphing and Writing Inequalities Holt Algebra 1

3 -1 Graphing and Writing Inequalities Example 2: Graphing Inequalities Graph each inequality. Draw a solid circle at 2. A. m ≥ -2 – 0 1 2 3 Shade all the numbers greater than 2 and draw an arrow pointing to the right. 3 B. t < 5 Simplify. Draw an empty circle at 5. – 4 – 3 – 2 – 1 0 Holt Algebra 1 1 2 3 4 5 6 Shade all the numbers less than 5 and draw an arrow pointing to the left.

3 -1 Graphing and Writing Inequalities Example 3: Writing an Inequality from a Graph Write the inequality shown by each graph. x<2 Use any variable. The arrow points to the left, so use either < or ≤. The empty circle at 2 means that 2 is not a solution, so use <. x ≥ – 0. 5 Use any variable. The arrow points to the right, so use either > or ≥. The solid circle at – 0. 5 means that – 0. 5 is a solution, so use ≥. Holt Algebra 1

3 -1 Graphing and Writing Inequalities Check It Out! Example 3 Write the inequality shown by the graph. x < 2. 5 Holt Algebra 1 Use any variable. The arrow points to the left, so use either < or ≤. The empty circle at 2. 5 means that 2. 5 is not a solution, so use <.

3 -1 Graphing and Writing Inequalities Reading Math “No more than” means “less than or equal to. ” “At least” means “greater than or equal to”. Holt Algebra 1

3 -1 Graphing and Writing Inequalities Example 4: Application Ray’s dad told him not to turn on the air conditioner unless the temperature is at least 85°F. Define a variable and write an inequality for the temperatures at which Ray can turn on the air conditioner. Graph the solutions. Let t represent the temperatures at which Ray can turn on the air conditioner. Turn on the AC when temperature t ≥ t 85 70 75 Holt Algebra 1 80 85 is at least 85°F 90 85 Draw a solid circle at 85. Shade all numbers greater than 85 and draw an arrow pointing to the right.

3 -1 Graphing and Writing Inequalities Lesson Quiz: Part II 5. A cell phone plan offers free minutes for no more than 250 minutes per month. Define a variable and write an inequality for the possible number of free minutes. Graph the solution. Let m = number of minutes 0 ≤ m ≤ 250 0 Holt Algebra 1 250