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 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

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

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

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

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!

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

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

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

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

Writing and Solving Inequalities 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 $9 number of guests x Mx + b ≤ y mx + b = y 9x + b ≤ y

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

Writing and Solving Inequalities 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 9x + 250 ≤ 450 9x ≤ 200 x ≤ 22 x ≤ 22.22 -250 -250 9 9

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?

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?