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Solving Two-Step and Multi-Step Inequalities. 3-4. Holt Algebra 1. Warm Up. Lesson Presentation. Lesson Quiz. Warm Up Solve the equation. 1. 2 x – 5 = –17. –6. Solve the inequality and graph the solutions. t > –4. 2. t-5 > -9. Essential Questions.

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  1. Solving Two-Step and Multi-Step Inequalities 3-4 Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz

  2. Warm Up Solve the equation. 1. 2x – 5 = –17 –6 Solve the inequality and graph the solutions. t > –4 2. t-5 > -9

  3. Essential Questions How are inverse operations used to solve inequalities? How can the solution of an inequality be graphed on a number line? How can inequalities be applied to real world situations?

  4. Objective 1.) Solve inequalities that contain more than one operation. 2.) Identify critical information from real world application word problems and set up the inequalities from the key information. 3.) Solve the multi-step inequalities.

  5. Inequalities that contain more than one operation require more than one step to solve. Use the appropriate inverse operations to undo the operations in the inequality one step at a time. The process involved is almost identical to the process for solving equalities.

  6. 45 + 2b > 61 –45 –45 b > 8 0 2 4 6 8 10 14 20 12 18 16 Example 1-A: Solving Multi-Step Inequalities Solve the inequality and graph the solutions. 45 + 2b > 61 Since 45 is added to 2b, subtract 45 from both sides to undo the addition. 2b > 16 Since b is multiplied by 2, divide both sides by 2 to undo the multiplication.

  7. –12 ≥ 3x + 6 – 6 – 6 –8 –10 –6 –4 0 2 4 6 8 10 –2 Check It Out! Example 1-B Solve the inequality and graph the solutions. –12 ≥ 3x + 6 Since 6 is added to 3x, subtract 6 from both sides to undo the addition. –18 ≥ 3x Since x is multiplied by 3, divide both sides by 3 to undo the multiplication. –6 ≥ x

  8. daily cost at We Got Wheels Cost at Rent-A-Ride must be less than $0.20 per mile # of miles. plus times 55 < 38 m + 0.20  Real World Example 1: Rental Cars To rent a certain vehicle, Rent-A-Ride charges $55.00 per day with unlimited miles. The cost of renting a similar vehicle at We Got Wheels is $38.00 per day plus $0.20 per mile. For what number of miles in the cost at Rent-A-Ride less than the cost at We Got Wheels? Let m represent the number of miles. The cost for Rent-A-Ride should be less than that of We Got Wheels.

  9. 55 < 38 + 0.20m –38 –38 Real World Example 1: Rental Cars 55 < 38 + 0.20m Since 38 is added to 0.20m, subtract 8 from both sides to undo the addition. 17 < 0.20m Since m is multiplied by 0.20, divide both sides by 0.20 to undo the multiplication. 85 < m Rent-A-Ride costs less when the number of miles is more than 85.

  10. Check a number greater than 85. Check the endpoint, 85. 55 = 38 + 0.20m 55 < 38 + 0.20m 55 38 + 0.20(85) 55 < 38 + 0.20(90) 55 38 + 17 55 < 38 + 18  55 55  55 < 56 Real World Example 1: Rental Cars Check

  11. Cost of lowest price shoes Amount she has saved must be greaterthan $8.50 per hour # of hours. times plus ≥ 150 + 31 h 8.5  Real World Example 2: Wages & Shopping Erykah has found three pairs of running sneakers that she likes, costing $150, $159, and $179. She has saved $31 already, and she has a job where she earns $8.50 per hour. How many hours will she have to work in order to afford any of these sneakers? Let h represent the number of hours she needs to work to buy any of the shoes.

  12. 8.5h + $31 ≥ $150 –31 –31 Real World Example 2: Wages & Shopping 8.5h + $31 ≥ $150 Since 31 is added to 8.5h, subtract 31 from both sides to undo the addition. 8.5h ≥ $150 Since m is multiplied by 8.5, divide both sides by 8.5 to undo the multiplication. 8.5h≥ $129 8.58.5 h > 14 Erykah will have to work at least 14 hours to buy the lowest priced shoes of $150. If she works more hours she will be able to afford the more expensive shoes.

  13. Check a number greater than 14. Check the endpoint, 14. 8.5h + $31 = $150 8.5h + $31 > $150 8.5(14) + 31 150 8.5(16)+31 > 150 119 + 31 150 136 + 31 > 150  150 = 150 166 > 150  Real World Example 2: Wages & Shopping Check

  14. Base starting Fare must be less than Amount she has. $0.65 per mile # of miles. times plus < $10 + $1.75 m 0.65  Real World Example 3: Yoh Taxi! Yellow Cab Taxi charges a starting rate of $1.75 an additional $0.65 per mile traveled. Katie has no more than $10 to spend on her cab fare. How many miles can Katie travel without going over her budget? Let m = the number of miles she can travel.

  15. 0.65m + $1.75< $10 –1.75 –1.75 Real World Example 3: Yoh Taxi! 0.65m + $1.75< $10 Since 1.75 is added to 0.65m, subtract 1.75 from both sides to undo the addition. 0.65m < $8.25 Since m is multiplied by 0.65, divide both sides by 0.65 to undo the multiplication. 0.65m<$8.25 0.650.65 m < 12 Since m= 12.69. Katie can travel 12 miles or less before reaching her budget limit of $10.

  16. Check a number greater than 14. Check the endpoint, 14. 8.5h + $31 = $150 8.5h + $31 > $150 8.5(14) + 31 150 8.5(16)+31 > 150 119 + 31 150 136 + 31 > 150  150 = 150 166 > 150  Real World Example 3: Yoh Taxi! Check

  17. is greater than or equal to First test score second test score divided by number of scores total score plus 90 ≥  (95 x) 2 + Real World Example 4: Grades The average of Jim’s two test scores must be at least 90 to make an A in the class. Jim got a 95 on his first test. What grades can Jim get on his second test to make an A in the class? Let x represent the test score needed. The average score is the sum of each score divided by 2.

  18. –95 –95 Real World Example 4: Grades Since 95 + x is divided by 2, multiply both sides by 2 to undo the division. 95 + x ≥ 180 Since 95 is added to x, subtract 95 from both sides to undo the addition. x ≥ 85 The score on the second test must be 85 or higher.

  19. 90 90   90 90 90.5 ≥ 90 Real World Example 4: Grades Check Check a number greater than 85. Check the end point, 85.

  20. Lesson TOTD: Part I Solve each inequality and graph the solutions. 1. 21 + 2x ≤ 13 x ≤–4 2. 2 + 3p> -11 p > –3

  21. Cost of Video Rentals must be more than Membership Fee of Plan-B Member-ship Fee Plan-A plus > $40 $25 + $1.25m Lesson TOTD: Part II 3. A video store has two movie rental plans. Plan A includes a $25 membership fee plus $1.25 for each movie rental. Plan B costs $40 for unlimited movie rentals. For what number of movie rentals is plan B less than plan A? Let m represent the number of movie rentals. What is the number of movie rentals on plan A that the cost will still be more than that the cost of B video plan.

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