Solving Inequalities

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Solving Inequalities

• Signature Instructional Plan 7

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Algebra I SIP 7 Solving InequalitiesTEKS
Addressed

• (c.3.A) The student analyzes situations
  involving linear functions and formulates linear
  inequalities to solve problems.
• (c.3.B) The student investigates methods for
  solving linear inequalities using concrete
  models, graphs, and the properties of equality
  selects a method and solves the inequalities.
• (c.3.C) For given contexts, the student
  interprets and determines the reasonableness of
  solutions to linear inequalities

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Activity 7-1Introduction to Inequalities

• Overview Students use problem situations and
  technology to explore linear inequalities
• In this lesson you will analyze situations
  involving inequalities in one variable and learn
  how to find and graph their solutions

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Activity 7-1Introduction to Inequalities

• An inequality is a statement that one quantity is
  less than or greater than another. We can write
  inequalities using mathematical symbols
• less than, smaller than lt
• greater than, larger than, more than gt

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Activity 7-1Introduction to Inequalities

• less than or equal to at most lt
• greater than or equal to at least gt
• Between __ lt x lt __

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Activity 7-1Introduction to Inequalities

• Write the inequality for the given situation and
  graph on a number line.
• You should drink at least six glasses of water a
  day.

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Activity 7-1Introduction to Inequalities

• To wrestle in this class, my weight must be
  between 125 150 lbs.

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Activity 7-2Investigating Inequalities

• You solve inequalities very much like you solve
  equations. You use the same strategies using
  inverse operations. However, there is one
  exception you need to remember when solving
  inequalities. We will explore this exception
  later toady in Investigation 2.
• Working with inequalities is very much like
  working with equations. Remember, however, that
  an equation shows a balance between two
  quantities, but an inequality shows an imbalance.

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Activity 7-2Investigating Inequalities

• Bianca and Joe are starting their own pet
  grooming business called Bianca and Joes. They
  have figured that they can spend no more than 50
  a month on flea shampoo. Joe has found a local
  dealer of pet shampoo, The Pet Pantry, who sells
  quart bottles for 4.00 a bottle plus a 5.00
  handling fee per month

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Activity 7-2Investigating Inequalities

• Write an inequality that represents the amount
  Bianca and Joes is willing to pay per month for
  The Pet Pantrys shampoo and solve.
• Answer questions 1-5 on your paper.

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Activity 7-2Investigating Inequalities

• Bianca is wondering if they can save money by
  shopping around. She found another local dealer,
  The Canine Corner, who sells the shampoo for
  3.00 a quart bottle plus a 15.00 handling
  charge per month.

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Activity 7-2Investigating Inequalities

• Write an inequality that represents when it is
  less expensive to buy an order with The Pet
  Pantry compared to The Canine Corner. (Hint
  your inequalitiy will involve your two
  expressions for the cost of shampoo from each
  store).
• Complete 6-12 on your own paper.

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Activity 7-2Investigating Inequalities

• 2.00 is deducted from Michaels PayPAM account
  each day for lunch. His balance at the beginning
  of January was 35.00. Pay PAMS will
  automatically send out an email reminding Michael
  to add money to his account when his balance
  drops below 15.

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Activity 7-2Investigating Inequalities

• How many lunches can Michael eat before PayPAM
  will send out the email?
• In order to solve the inequality in Investigation
  2 above, you must learn the following rule about
  solving inequalities whenever you multiply or
  divide by a negative number, you must reverse the
  inequality sign.

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Activity 7-3Solving Inequalities

• Complete this sentence When solving
  inequalities, you must reverse the inequality
  sign whenever you

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Activity 7-3Solving Inequalities

• Domain
• ____ lt ____
• Range
• ____ lt ____

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Activity 7-3Solving Inequalities

• Luis is working part-time after school for a pool
  and spa cleaning company. He makes 6.00 per
  hour. He is saving money for his prom expenses
  which he expects to be about 300.
• Write and solve an inequality for the least
  number of hours he needs to work to achieve his
  goal. Graph the solution set.

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Activity 7-5Investigating Inequalities II

• We have been solving inequalities and graphing
  the solution on a number line. However,
  everything we have learned about linear functions
  applies to inequalities as well. Today we will
  use a familiar scenario to learn how to graph
  inequalities on a coordinate plane

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Activity 7-5Investigating Inequalities II

• Write a function rule that represents the amount
  of money charged by the Pet Pantry for an order
  of shampoo. Graph the rule.

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Activity 7-5Investigating Inequalities II

• Bianca and Joe decide to spend up to 50.
• Write the inequality.
• Sketch the graph of the solution

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Activity 7-5Investigating Inequalities II

• Bianca and Joe want to spend at least 50.
• Sketch the graph.
• Write the inequality.

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Activity 7-6Limiting Driving Miles

• Vince reads that cars are a major source of air
  pollution. He decides to look at his family's
  driving habits. They have two vehicles, a car and
  an SUV. His parents estimate that the family
  drives about 1,200 miles each month. They decide
  to try to limit their driving to no more than
  1,000 miles each month.

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Activity 7-6Limiting Driving Miles

• Write the inequality used to determine possible
  pairs that give a total of no more than 1,000
  miles.
• Solve the inequality for y.
• What is your independent and dependent variables?

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Activity 7-6Limiting Driving Miles

• Graph the inequality.
• Write an inequality to describe the domain for
  this situation.
• Write an inequality to describe the range for
  this situation

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Activity 7-7Linear Inequality Models

• The CamelTote Company makes backpacks. They make
  a profit of 3 for each nylon backpack and 10
  for each canvas backpack. How many backpacks
  must the company sell to make a profit of more
  than 250?

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Activity 7-7Linear Inequality Models

• Write a linear inequality to describe the
  situation.
• What is your independent variable?
• What is your dependent variable?
• Graph the linear inequality.

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Activity 7-7Linear Inequality Models

• Write three possible solutions to the problem.
• Why is 10 nylon packs and 22 canvas packs not a
  solution?

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Activity 7-7Linear Inequality Models

• You are shopping for black and silver crepe paper
  to decorate the cafeteria for a school dance.
  Silver crepe paper cost 5 per roll and black
  crepe paper costs 3 per roll. You have at most
  48 to spend. How much black and silver crepe
  paper can you buy?

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Activity 7-7Linear Inequality Models

• Write a linear inequality to describe the
  situation.
• What is your independent variable?
• What is your dependent variable?
• Graph the linear inequality

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Activity 7-7Linear Inequality Models

• What is the greatest number of rolls of black
  crepe paper you can buy?
• What is the greatest number of rolls of silver
  crepe paper you can buy?