Inequalities It is … Tuesday!!! • Take out your homework and a red pen • Period 2: Take out your notes from Friday!!! • Take out your Review Packet and have it on your desk – Ms. Huls will walk around RIGHT when the bell rings to see if you printed off the Review Packet – It needs to be on your desk to get the full 5 points 3.1: Inequalities Learning Objective SWBAT solve inequalities VOCAB • inequality: – a math sentence that contains the symbols • Solution of an inequality – Any number that makes the inequality true Word Bank: Translating Practice: Whiteboards • a number y is greater than 4 ___________________________ • a number c is less than or equal to 2 ___________________________ • a number m is at least 3 ___________________________ • In many states, you must be at least 16 years old to obtain a driver’s license • Ms. Huls makes more than 75 copies each day Identifying Solutions x> 6 X= 6 X=0 x= -4 Whiteboards Graphing Inequalities Graph c > -2 Graph 4 < m Write an inequality from a Graph Write an inequality from a Graph Write an inequality from a Graph • Equivalent inequality – Inequalities with the same solution • EX: Solve each Inequality: Whiteboards 1. X-3 < 5 2. 12 < X -5 3. Y +5 < -7 Investigate!!!! Do this in your notes! Answer all the questions Red Flag Alert When you multiply or divide by a negative number, you need to FLIP the inequality sign! WHITEBOARDS Write an inequality for each situation. 1. The temperature must be at least –10°F. 2. The temperature must be no more than 90°F. x ≤ 90 Solve each equation. 3. x – 4 = 10 4. 15 = x + 1.1 14 13.9 x ≥ –10 Whiteboards Solve each equation. 1. –5a = 30 2. 3. 4. Graph each inequality. 5. x ≥ –10 6. x < –3 WHITEBOARDS! Solve each inequality and graph the solutions. 1. 8x < –24 3. x < –3 x > 20 2. –5x ≥ 30 4. x ≤ –6 x≥6 PROBLEM SOLVING Sami has a gift card. She has already used $14 of the of the total value, which was $30. Write, solve, and graph an inequality to show how much more she can spend. 1 Understand the Problem The answer will be an inequality and a graph. List important information: • Sami can spend up to, or at most $30. • Sami has already spent $14. 2 Make a Plan Write an inequality. Let g represent the remaining amount of money Sami can spend. Amount remaining plus g + g + 14 ≤ 30 amount used 14 is at most ≤ $30. 30 3 Solve Since 14 is added to g, subtract 14 from both sides to undo the addition. g + 14 ≤ 30 – 14 – 14 g + 0 ≤ 16 g ≤ 16 It is not reasonable for Sami to spend a negative amount of money, so graph numbers less than or equal to 16 and greater than 0. 0 2 4 6 8 10 12 14 16 18 10 Additional Example 3: Consumer 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. Let x represent the amount Mrs. Lawrence can add to the bid. $475 plus 475 + 475 + x ≤ 550 amount can add x is at most ≤ $550. 550 WORD PROBLEM!!! Jill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy? Let p represent the number of tubes of paint that Jill can buy. $4.30 times 4.30 • number of tubes p is at most $20.00. ≤ 20.00 Jill has a $20 gift card to an art supply store where 4 oz tubes of paint are $4.30 each after tax. What are the possible numbers of tubes that Jill can buy? 4.30p ≤ 20.00 Since p is multiplied by 4.30, divide both sides by 4.30. The symbol does not change. p ≤ 4.65… Since Jill can buy only whole numbers of tubes, she can buy 0, 1, 2, 3, or 4 tubes of paint. A pitcher holds 128 ounces of juice. What are the possible numbers of 10-ounce servings that one pitcher can fill? Let g represent the number of servings of juice the pitcher can contain. 10 oz times number of servings is at most 128 oz 10 • g ≤ 128 A pitcher holds 128 ounces of juice. What are the possible numbers of 10-ounce servings that one pitcher can fill? 10g ≤ 128 Since g is multiplied by 10, divide both sides by 10. The symbol does not change. g ≤ 12.8 The pitcher can fill 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12 servings. WHITEBOARDS A soccer coach plans to order more shirts for her team. Each shirt costs $9.85. She has $77 left in her uniform budget. What are the possible numbers of shirts she can buy? Lesson Quiz: Part I Solve each inequality and graph the solutions. 1. 13 < x + 7 x>6 2. –6 + h ≥ 15 h ≥ 21 3. 6.7 + y ≤ –2.1 y ≤ –8.8 Lesson Quiz: Part II 4. A certain restaurant has room for 120 customers. On one night, there are 72 customers dining. Write and solve an inequality to show how many more people can eat at the restaurant. x + 72 ≤ 120; x ≤ 48, where x is a natural number