inequalities < > t - ms. schmidt's math...
TRANSCRIPT
Name Grade Teacher Ms. Schmidt
Inequalities
< >
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
Greater than or equal to
At Least
Minimum
Less than Less than or equal to
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
Greater than or equal to
At Least
Minimum
Less than Less than or equal to
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
Solving Inequalities Classwork Day 4
Directions: Solve, and graph the given inequality.
Solving Inequalities Classwork Day 4
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.
Inequality __________________________ Solve the inequality
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.
Inequality __________________________ Solve the inequality
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.
Inequality __________________________ Solve the inequality
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.
Inequality __________________________ Solve the inequality
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.
Inequality __________________________ Solve the inequality
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.
Inequality __________________________ Solve the inequality
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?
Inequality __________________________ Solve the inequality
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