Intro to Inequalities

≥

≤

˂

>

Credit CardSituation 1: Your mom gave you her credit card

and said that you could go shopping for a birthday present for your girlfriend (or boyfriend). She said that you could spend no more than $125.

1. List at least 5 of the amounts that you could spend.

2. You saw an awesome cell phone that was priced at $130? Can you buy it?

Explain your thinking.

Credit CardSituation 1: Your mom gave you her credit card

and said that you could go shopping for a birthday present for your girlfriend (or boyfriend). She said that you could spend no more than $125.

3. What is the maximum amount that you could spend on the present and still be following your mom's instructions?

4. Is there just one correct amount that you could spend?

Credit CardSituation 1: She said that you could spend no

more than $125.

What other words could we use for this?

Less than or Less than or equal to 125equal to 125

No more No more than 125than 125

Up to 125Up to 125

Maximum Maximum of 125of 125

x ≤ 125

same as

125 ≥ x

Using Inequality symbols helps to represent all the possibilities that you could spend.

Symbolic: spending (x) 125

Credit CardSituation 2: What if your mom said that you had

to spend at least $125 on the present.

1. List no less than 4 of the possibilities that you could spend.

2. What is the least you could spend on the present and still be following your mom's instructions?

3. What is the most you could spend on the present and still be following your mom's instructions?

Credit CardSituation 2: What if your mom said that you

had to spend at least $125 on the present.

What other words could we use for this?

Greater than Greater than or equal to or equal to

125125

At least 125At least 125 125 or more125 or more

Minimum Minimum of 125of 125

x ≥ 125

same as

125 ≤ x

Symbolic: spending (x) 125

Fill in each column with Fill in each column with phrases that best describe phrases that best describe

the inequalitythe inequality

< < << > > >> LESS THAN GREATER

THAN

LESS THAN OR EQUAL TO

GREATER THAN OR EQUAL TO

SMALLER THAN

BIGGER THAN

MAXIMUM OFMINIMUM OF

UP TOAT LEASTNO MORE

THANNO LESS THAN

AT MOST

NAME THAT NUMBERNAME THAT NUMBER

What is a compound inequality? ____________________________

______________________________________________________________________________.

Situation 3: Contestants on American idol must be between the ages of 15 and 28.

1. List at least 5 of the ages a contestant could be.

Situation 3: Contestants on American idol must be between the ages of

15 and 28.

2. What is the youngest you could be and how could you describe that as an inequality?

3. What is the oldest you could be and how could you describe that as an inequality?

4. How could you write this situation using inequalities?

Write inequalities based on the situations below:

1) Jason can spend up to $95 on his Dad’s credit card

2) Ella must have an 85 or over in MMA to get her car back

3) Dana must not fail more than 2 classes this year in order to graduate

4) Sam needs to score better than 98 on his next English quiz to get an A average

5) Angel cannot spend more than 2 and a half hours on her homework

6) John may watch up to half an hour of TV per day

7) If Aaron uses more than 600 minutes on his cell phone each month, he pays a $20 penalty

8) Catherine has to smile 5 or more times a day at work in order to get a $100 bonus

HomeworkHomework

Pg. 171 #1-5, 18-21, 34-37, 46-49Pg. 171 #1-5, 18-21, 34-37, 46-49 Pg. 206 #2, 15, 28, 30-35Pg. 206 #2, 15, 28, 30-35

Inequality symbols allow us to represent situations that have ___________________________.

You use them instead of ___________________________.

What is a solution to an inequality? ___________________________________________________.

Try It1. You can receive a maximum of 3 absences to exempt the final exam.

numbers_______, _______, _______ Inequality____________________

2. Your semester average for the class needs to be at least an 80 to exempt the final exam.

numbers_______, _______, _______ Inequality____________________

3. To pass Algebra you can have no less than a 70 average for the entire school year.

numbers_______, _______, _______ Inequality____________________

4. To ride on the roller coaster, Texas Cyclone, you must be taller than 40 inches.

numbers_______, _______, _______ Inequality____________________