Unit - Algebra
Guided Notes - Inequalities
INEQUALITIY SYMBOLS
Date_____________
Greater than ________
Less than ___________
Greater than or equal to ________
Less than or equal to _________
To check if a number is a solution to an inequality, __________________________________
1) Are the following
numbers a solution to the
inequality x + 4 > 6
x=3
x=0
x=4
x=2
2) Are the following numbers a
solution to the inequality ½x 6
x = 12
x=0
x = 14
x=3
4) Which value for x makes the inequality
-2x + 6 < 10 true?
3)
A. -4
B. -3
C. -2
D. 0
When you are graphing an inequality on a number line, you are illustrating any possible
___________________________ to the inequality.
1. Draw a circle around the number that x is compared to.
2. When it is > or < Leave the circle _______
When it is ≤ or ≥ ________the circle
3. Shade all numbers that satisfy the inequality
Example: x > 4
1)
3)
2)
4)
a>5
To Write an Inequality:
1.
See if the circle is ________________________ or open
If closed ________ or _______
If open _________ or _______
2. See if the numbers shaded or above (_________________than) or below
(_______________________than) the number circled
Write Inequalities for the Following Examples:
1) ________
3) ________
2) _________
4) _________
Word Problems:
1) You must be at least 18 years of age to vote. Write and graph an inequality for this
requirement.
Inequality __________
2) Write an inequality for “To qualify for the race, you time can be at most 62 seconds.”
Inequality __________
3) Kamisha got several bills in the mail today: her rent, which is $425; her water bill, which
is $25; and her phone bill, which is $15. She says she does not have enough money in the
bank to cover these expenses. Write an inequality to represent the amount of money in
her account.
Inequality __________
Unit - Algebra
Guided Notes – Solving Inequalities
Date_____________
1)
Draw lines around the ________________ symbol
2)
Solve as if it is a _______________ equation
3)
Bring down the ___________ symbol unless you multiply or divide by a
______________-________ number, in which case your sign _________________.
Examples:
Solve and Graph Inequalities:
1.
3x + 2 > 8
x___________
3. ____________________
___________
2. ____________________
___________
4. ____________________
___________
5. ____________________
___________
7. ____________________
___________
9. ____________________
___________
OAA Practice:
6. ____________________
___________
8. ____________________
___________
10. ____________________
___________
Unit - Algebra
Guided Notes – Inequality Word Problems
Key Words:
Date_____________
Greater Than _____________________________________________________________
Greater Than or Equal To ____________________________________________________
Less Than ________________________________________________________________
Less Than or Equal To _______________________________________________________
Examples:
1) Jill charges a base rate of $25 plus $18 for
each hour she mows the lawn. Write an
equation to find the number of hours Jill
must work in order to earn at least $115.
2) Yellow Cab Taxi charges a flat fee of $2
and an additional $0.50 per mile. Kate has
no more than $10 to spend on her ride.
Write an inequality for the situation. How
far can Kate go without exceeding her limit?
Inequality___________________
x__________
Inequality____________________
___________
Percent Decrease
1) An item is 30% off. If Janae wants to
spend at most $35, write an inequality to
represent the most she could spend on the
item.
2) Jarod is online shopping at a site where
everything is marked 20% off. He has a
coupon for free shipping but he can only use
it if he spends at least $50. What is the
minimum amount of the original item?
Inequality____________________
___________
Inequality____________________
___________
Percent Increase
1) Lilly gets a raise of 5%. She says “I’ll be Inequality____________________
making at least 42,000!” If this is true, what
___________
was her minimum salary before the raise?
2) Jaxson is eating at J Alexander’s. He
wants to tip the waitress 20% and says
“With tip, I can only spend at most $30.”
What is the maximum amount Jaxson can
spend on his meal?
Inequality____________________
___________