Warm Up Compare. Write <, >, or =. 1. –3 2 3. < 2. 6.5 6.3 1. –3 2 3. < 2. 6.5 6.3 > > 4. 0.25 = Tell whether the inequality x < 5 is true or false for the following values of x. 5. x = –10 T 6. x = 5 F 7. x = 4.99 T 8. x = T

An inequality is a statement that two quantities are not necessarily equal. The quantities are compared by using the following signs: ≤ A ≤ B < A < B > A > B ≥ A ≥ B ≠ A ≠ B A solution of an inequality is any value of the variable that makes the inequality true.

Example 1: Graphing Inequalities Graph each inequality. A. m ≥ B. t < 5(–1 + 3)

Example 2: Writing an Inequality from a Graph Write the inequality shown by each graph.

Reading Math “No more than” means “less than or equal to.” “At least” means “greater than or equal to”.

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.

Check It Out! Example 4 A store’s employees earn at least $8.50 per hour. Define a variable and write an inequality for the amount the employees may earn per hour. Graph the solutions.

Example 5: Using Addition and Subtraction to Solve Inequalities Solve the inequality and graph the solutions. a) x + 12 < 20 b) d – 5 > –7 c) 0.9 ≥ n – 0.3

Example 6: Problem-Solving Application Sami has a gift card. She has already used $14 of the total value, which was $30. Write, solve, and graph an inequality to show how much more she can spend.

Check It Out! Example 6 The Recommended Daily Allowance (RDA) of iron for a female in Sarah’s age group (14-18 years) is 15 mg per day. Sarah has consumed 11 mg of iron today. Write and solve an inequality to show how many more milligrams of iron Sarah can consume without exceeding RDA.

Example 7: Application Mrs. Lawrence wants to buy an antique bracelet at an auction. She is willing to bid no more than $550. So far, the highest bid is $475. Write and solve an inequality to determine the amount Mrs. Lawrence can add to the bid. Check your answer.

Check It Out! Example 7 Josh wants to try to break the school bench press record of 282 pounds. He currently can bench press 250 pounds. Write and solve an inequality to determine how many more pounds Josh needs to lift to break the school record. Check your answer.

Homework: Page 103 #26-37; Page 109 #7-15, 16- 22 even, 25, 31, 34-37