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Writing and Solving Inequalities

Writing and Solving Inequalities. Writing and Solving Inequalities. Lesson Objective: 4.01 Students will know how to write and solve an inequality from a word problem. Writing and Solving Inequalities.

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Writing and Solving Inequalities

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  1. Writing and Solving Inequalities

  2. Writing and Solving Inequalities • Lesson Objective: 4.01 • Students will know how to write and solve an inequality from a word problem

  3. Writing and Solving Inequalities • A local restaurant will deliver food to your house if the purchase amount of your order is at least $25. The total for part of your order is $17.95. must you spend for the restaurant to deliver your order? • First, look at the question, what is it asking? • How much more money How much more

  4. Writing and Solving Inequalities • A local restaurant will deliver food to your house if the purchase amount of your order is $25. The total for part of your order is $17.95. How much more must you spend for the restaurant to deliver your order? • What does the term “at least” mean? • It means it can’t be less than but it can be equal to • Total purchase ≥ $25 at least

  5. Writing and Solving Inequalities • A local restaurant will deliver food to your house if the purchase amount of your order is at least $25. The total for part of your order is . How much more must you spend for the restaurant to deliver your order? • How much have you already purchased? • We need to find out how much more we need to add to the order to get at least $25 so we call that x. $17.95 Total purchase ≥ 25 17.95 + x ≥ 25

  6. Writing and Solving Inequalities • Subtract 17.95 from both sides • x has to be at least 7.05 • Therefore you have to purchase $7.05 or more to get delivery 17.95 + x ≥ 25 x ≥ 7.05 -17.95-17.95

  7. Writing and Solving Inequalities • The maximum load for a certain elevator is 2000 pounds. The total weight for the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight w. How much must the crate weigh in order to not exceed the weight of the elevator? You Try!

  8. Writing and Solving Inequalities • The maximum load for a certain elevator is 2000 pounds. The total weight for the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight w. How much must the crate weigh in order to not exceed the weight of the elevator? • “Maximum weight” means less than or equal to • Total weight ≤ 2000 pounds

  9. Writing and Solving Inequalities • The maximum load for a certain elevator is 2000 pounds. The total weight for the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight w. How much must the crate weigh in order to not exceed the weight of the elevator? • Passengers weight 1400, delivery man weighs 243, we don’t know the crate’s weight so we call it w. • Add them together to see if they’re under 2000 Total weight ≤ 2000 1400 + 243 + w ≤ 2000

  10. Writing and Solving Inequalities • Combine like terms: add the numbers together on the left side • Subtract 1643 from both sides • The weight of the crate has to be less than or equal to 357 pounds 1400 + 243 + w ≤ 2000 1643 + w ≤ 2000 W ≤ 357 -1643-1643

  11. Writing and Solving Inequalities • A banquet hall charges a flat rate of $250 plus $9 per person in attendance. The Wilsons wish to spend no more than $450 for their retirement party. What is the maximum number of guests they can invite? More Practice

  12. Writing and Solving Inequalities $9 • A banquet hall charges a flat rate of $250 plus per person in attendance. The Wilsons wish to spend no more than $450 for their retirement party. What is the maximum they can invite? • Maximum means less than or equal to, so change the = • What don’t we know? • What do we call something we don’t know? • $9 goes with x so we replace m with 9 number of guests x mx + b = y Mx + b ≤ y 9x + b ≤ y

  13. Writing and Solving Inequalities • A banquet hall charges a flat rate of $250 plus $9 per person in attendance. The Wilsons wish to spend no more than $450 for their retirement party. What is the maximum number of guests they can invite? • The total is $450 so replace the y with 450 • The banquet hall charges $250 no matter how many guests, so it’s the constant, or b 9x + 250 ≤ 450 9x + b ≤ y 9x + b ≤ 450

  14. Writing and Solving Inequalities 9x + 250 ≤ 450 9x ≤ 200 x ≤ 22.22 x ≤ 22 • Subtract 250 from both sides • Divide both sides by 9 • Since we are looking to spend less than $450 we round the answer down • Therefore the Wilsons can only invite 22 people to the event -250-250 9 9

  15. Writing and Solving Inequalities • Jay has lost his mother’s favorite necklace so he will rent a metal detector to try to find it. A rental company charges a one-time rental fee of $15 plus $2 per hour to rent a metal detector. Jay has only $35 to spend. What is the maximum amount of time he can rent the metal detector?

  16. Writing and Solving Inequalities • The average of Jim’s two tests scores must be at least 90 to make an A in the class. Jim got a 95 on his first test. What is the lowest grade Jim can get on his second test to make an A in the class?

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