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. How much more
must you spend for the restaurant to deliver your
order?
 First, look at the question, what is it asking?
 How much more money
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. 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
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. 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.
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
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?
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
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
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?
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?
x
 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
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
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
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?