Warm-up: Answer the following questions as accurately as you can: 1) What are 3 values that are less than 10? _____________ 2) What are 3 values that are greater than –150? ________ 3) How much money does a “rich” person have? 4) When someone has a fever, what temperature do they have? 5) How tall do you think you have to be to ride Drop Zone?

3-1 Graphing & Writing Inequalities

Compare. Write, or =. 1)10 ____ 212) 5.27 ___ ) 20% ____0.24) –4 ____ –5 <> =>

An inequality is a… …mathematical statement that compares two quantities using one of the following signs: < >

EXAMPLE 1: Applications with Inequalities 1A) Jimmy’s dad told him not to turn on the air conditioner unless the temperature was at least 82 degrees. Define a variable and write an inequality for the temperatures at which Jimmy can turn on the air conditioner. Graph the solutions. 82 Is 82 degrees included in the statement? If it’s 82 degrees, should he turn the AC on? 81 If it’s 81 degrees, should he turn the AC on? Yes, fill in the end point at If it’s 83 degrees, should he turn the AC on? x = temperature x 82

EXAMPLE 1: Applications with Inequalities 1B) The maximum speed allowed on the highway is 65 miles per hour. Define a variable and write an inequality for the situation. Graph the solutions. 65 Is 65 miles per hour included in the speed limit? Are you allowed to go 65 mph? 64 Are you allowed to go 64 mph? Yes. Fill in the end point at x = speed (mph) x 65

EXAMPLE 1: Applications with Inequalities 1C) It is recommended that the pool capacity at the community pool stay under 100 people. Define a variable and write an inequality for the situation. Graph the solutions. 100 Is 100 included in the possible number of people allowed in the pool? If you were the 100 th person to try to get in the pool, should they allow you in? 99 Are 99 people allowed? NO. Leave the end point empty. 101 x = # of people x 100 (only whole #s)

The solution of an inequality is… … ANY value that makes the inequality true , Example: Solutions:

An inequality, such as x < 3, has too many solutions to list (an infinite # of solutions). One way to show all the solutions is to use a graph on a number line. + – 3 4 2

Inequality Signs < less than > more than When graphing: less than equal to more than equal to NOT equal Empty circle Shaded circle Empty circle under over Maximum, No more than At least, No less than

EXAMPLE 2: Graphing Inequalities 2A) Rewrite w/variable on the LEFT Use a straight edge: draw # line Write the end point & put an empty or shaded circle Write a # on the left & right of the endpoint Use a line with an ARROW to show all solutions Step 6: _____________________ Check a solution If the variable is on the left, the inequality sign will point in the direction of the graph. You read this as: “All real #s greater than or equal to 5.” ENDPOINT + – ✔

EXAMPLE 2: Graphing Inequalities 2B) Rewrite with the variable on the LEFT Use a straight edge: draw # line Write the end point & put an empty or shaded circle Write a # on the left & right of the endpoint Use a line with an ARROW to show all solutions Step 6: _____________________ Check a solution If the variable is on the left, the inequality sign will point in the direction of the graph. You read this as: “All real #s less than –7.” + – ✔

EXAMPLE 2: Graphing Inequalities 2C) Rewrite with the variable on the LEFT Use a straight edge: draw # line Write the end point & put an empty or shaded circle. ¾ 1 ½ Write a # on the left & right of the endpoint Use a line with an ARROW to show all solutions Step 6: _____________________ Check a solution If the variable is on the left, the inequality sign will point in the direction of the graph. Practice saying it with a classmate. + – ✔

EXAMPLE 2: Graphing Inequalities 2D) Rewrite with right side simplified Use a straight edge: draw # line Write the end point & put an empty or shaded circle Write a # on the left & right of the endpoint Use a line with an ARROW to show all solutions Step 6: _____________________ Check a solution If the variable is on the left, the inequality sign will point in the direction of the graph. + – ✔

EXAMPLE 3: Writing an Inequality from a graph 3A) Endpoint: 11.5 How would we say what the graph shows? “All real #s less than or equal to 11.5” “Less than or equal to”

EXAMPLE 3: Writing an Inequality from a graph 3B) –4.2 –4.3 –4.1 Endpoint: –4.2 How would we say what the graph shows? “All real #s greater than –4.2”

EXAMPLE 3: Writing an Inequality from a graph 3C) Endpoint: 89 How would we say what the graph shows? “All real #s greater than or equal to 89”

Warm-up: Compare. Write, or =. 1)2) 3)4) 5) Tell whether the inequality x < 5 is true or false for the following values of x: a)x = –10b) x = 5c) x = 4.99d) x = –0.5 6) Solve: <> = < True False True x = –2

Review: Writing Inequalities Writing inequalities from words: “At least…” x ____“No more than…” x _____ “At most…” x ____“No less than…” x _____ “Maximum…” x ____“Under…” x ______

Additional Practice with Word Problems: Define a variable and write an inequality for each situation. Graph the solutions. 1) You must be at least 52” to ride Drop Zone at Great America. x = height

Additional Practice with Word Problems: Define a variable and write an inequality for each situation. Graph the solutions. 2) The maximum number of pieces of Halloween candy I can eat before I feel sick is 15. x = candy pieces