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Solving Inequalities

- Signature Instructional Plan 7

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

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

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

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 __

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.

Activity 7-1Introduction to Inequalities

- To wrestle in this class, my weight must be

between 125 150 lbs.

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.

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

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.

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.

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.

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.

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.

Activity 7-3Solving Inequalities

- Complete this sentence When solving

inequalities, you must reverse the inequality

sign whenever you

Activity 7-3Solving Inequalities

- Domain
- ____ lt ____
- Range
- ____ lt ____

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.

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

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.

Activity 7-5Investigating Inequalities II

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

Activity 7-5Investigating Inequalities II

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

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.

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?

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

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?

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.

Activity 7-7Linear Inequality Models

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

solution?

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?

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

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?

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