Inequalities < > t - Ms. Schmidt's Math...

Name Grade Teacher Ms. Schmidt

Inequalities

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Understanding Inequalities Classwork Day 1

Inequalities: ____________________________________________________________________________

- Inequalities vs. Equations

𝑛 − 5 < 10 𝑛 − 5 = 10

________________________________________________________________________

- Values that make an inequality true are only some of the solutions!

Types of Inequalities:

> <

Greater than

Greater than or equal to

At Least

Minimum

Less than Less than or equal to

At Most

Maximum

What values of x will make the inequality true?

1) x > 3 2) 3x 3) -4 > x 4) 1 < x

__________________ __________________ __________________ __________________

Determine which option(s) the variable could be. If none of the options can write ‘none’.

5) 10x + 3 < 92 6) 2x < 15 7) 7y > 70

A. 10 A. 6 A. 6

B. 4 B. 8 B. 9

C. 6 C. 1 C. 7

D. 2 D. 9 D. 8

8) 225 e 9) 10y > 57 10) 2e > 12

A. 3 A. 6 A. 1

B. 5 B. 8 B. 10

C. 8 C. 9 C. 4

D. 6 D. 1 D. 6

Understanding Inequalities Classwork Day 1

Try These:

Determine which option(s) the variable could be. If none of the options can write ‘none’,

Writing Inequalities Classwork Day 2

> <

Greater than


At Least

Minimum


At Most

Maximum

Sentence Inequality

1) x is greater than 3

2) You must be at least 16 to drive.

3) x is less than or equal to 3

4) 7 is greater than or equal to x.

5) You must be 60 inches or taller to ride the

roller coaster

6) 15 or less people can go on this bus

7) The pizza plus $2 tax is more than $10

8) You need to be 18 years or older.

Write an inequality to represent a situation.

9) Florencia has $60 to spend on clothes. She wants to buy a pair of jeans for $22 dollars and spend the

rest on t-shirts. Each t-shirt costs $8. Write an inequality for the number of t-shirts she can purchase.

10) As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at more

than $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Graphing Inequalities Classwork Day 3

> <

Greater than


At Least

Minimum


At Most

Maximum

When graphing use:

When graphing use:

When graphing use:

When graphing use:

Translate and graph for each inequality.

1) x > 3 2) 3x 3) -4 > x 4) 1 < x

__________________ __________________ __________________ __________________

Graphing Inequalities

We can represent a linear inequality in one variable on a number line.

We use the following symbols in the representation:

An ________________ circle is used for < and > to indicate that the number is not included.

A _________________ or filled-in circle is used for and to indicate that the number is included.

A line with an _______________ indicates that the line continues to ___________________ in the

direction of the arrow.

Guided Practice

Graph the following inequalities:

1) x 3 2) x < 5 3) 7 x 4) -2 > x

Graphing Inequalities Classwork Day 3

Write the inequality to represent the graph.

5) 6) 7) 8)

2 5 0 8

ans. ____________ ans. ____________ ans. ____________ ans. ____________

Independent Practice

1) Graph the following inequalities:

a) x 9 b) x < 7 c) 0 x d) 1 > x

2) Write the inequality to represent the graph.

a) b) c) d)

8 6 2 4

ans. ____________ ans. ____________ ans. ____________ ans. ____________

3) Translate and graph.

Sentence Inequality Graph

x is greater than 3

You must be at least 16 to drive.

x is less than or equal to 3

A number decreased by five is

less than fourteen.

Five times a number is at least

twenty.

Solving Inequalities Classwork Day 4

To solve inequalities, follow the same processes that apply to equations.

►Example

Graph the solution set for x 4 < 16

+ +

x <

Graph

Try These.

Directions: Solve, and graph the given inequality.

1. y + 3 4

2. x 4 > 12

3. 2n 2

4. 20 > 5x

5. 310

t

6. 16 8y

7. 54 > 6h

8. 104

t

9. x 2 80


Directions: Solve, and graph the given inequality.


Real-World Inequalities

9) The cost of a gallon of orange juice is $3.50. What is the maximum number of containers you can buy for

$15?

10) Which statement can be modeled by x + 3 12?

(1) Sam has 3 bottles of water. Together, Sam and Dave have at most 12 bottles of water.

(2) Jennie sold 3 cookbooks. To earn a prize, Jennie must sell at least 12 cookbooks.

(3) Peter has 2 baseball hats. Peter and his brothers have fewer than 12 baseball hats.

(4) Kathy swam 3 laps in the pool this week. She must swim more than 12 laps.

11) Your brother has $2,000 saved for a vacation. His airplane ticket is $637. Write and solve an inequality to

find out how much he can spend for everything else.

12) Your local bank offers free checking for accounts with a balance of at least $500. Suppose you have a

balance of $516.46 and you write a check for $31.96. How much do you need to deposit to avoid being

charged a service fee?

CONCLUSION

Why do we graph our solution of an inequality on a number line and we didn’t graph our answer in an

equation? (Explain in words)

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

Solving Inequalities Homework Day 4

Application Problems Classwork Day 5 Warm Up

1) Part A: Given the inequality: x + 4 12 Make up your own word problem to represent the inequality.

Part B: Solve the inequality. Part C: Graph the inequality.

1) A rental company charges $5 per mile to rent a car. Mr. DeMeo does not want to spend more than $100 for

his rental car. Write, solve and graph an inequality to find how many miles he can drive and not spend more

than $100. Interpret the solution.

Inequality __________________________ Solve the inequality

Graph the solution

2) Halfway through the bowling league season, Nick averages 2 strikes per game. Write, solve and graph an

inequality to find how many more games it will take for Nick to have at least 61 strikes, the league record.


Graph the solution

3) Tyler needs at least $205 for a new video game system. He has already saved $30. Write, solve and graph

an inequality to find how much more he will to buy the system.


Graph the solution

4) A plate weighs 4

1 pound. A shelf can hold at most 20 pounds. Write, solve and graph an inequality to find

how many plates the shelf can hold.


Graph the solution

Application Problems Homework Day 5

1) Katie is starting a babysitting business. She spent $26 to make signs to advertise. She charges $3 for each

hour of service. Write, solve and graph an inequality to find the number of hours she will have to babysit to

make a profit.


Graph the solution

2) As a salesperson, Audrey earns $5 per sale. This week, she wants to pay to be at least $125. Write, solve

and graph an inequality for the number of sales Audrey needs to make.


Graph the solution

3) Dylan and his sister went to the movies. They had $34 altogether and spent $9.50 per ticket. Dylan and his

sister bought snacks to share. Write, solve and graph an inequality for the amount they spent on snacks.


Graph the solution

4) Mrs. Smith decides to buy a pair of jeans and a sweater. She has $120 in her wallet. If the price of the jeans is $35, what is the highest possible price of the sweater?


Graph the solution

Mixed Review

Simplify the following expressions.

5) (22 + 19b) + 7 6) xx 8)69(2 7) 8)69(3

1 8) (12 + 4)3

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