1. Writing, Graphing, and Solving
Inequalities
Writing, Graphing, and Solving

2. What is an inequality?
An inequality compares two values that are not equal.
Inequalities have MORE THAN ONE solution.

3. Symbols < less than > greater than < less than or equal to
> greater than or equal to

5. Inequality Statements
“at least”
“no more than”
“at most”
“minimum of”
“maximum of”
“no less than”
”greatest”
“ up to”

6. x is greater than 5
-77 is greater than x
-11 is greater than or equal to x
x is less then or equal to 58
x is less than or equal to -47
x is equal to 65
-77 is less than x
x is greater than to equal to -7
x is greater than -8
x is less then -93

7. Swim practice will be no more than 35 laps.
The mountain is at least 985 feet tall.
The movie will be no more than 90 minutes in length.
Kevin ran for less than 5 miles.
The occupancy of the room must be less than 437 people.
You can not spend more than 50 dollars.
More than 800 fans attended the opening soccer game.
The heavyweight division is greater than 200 pounds.

11. End of today’s lesson

12. Write an inequality for the following:
1. More than 40,000 fans attended the opening football game at the University of Florida.
2. Her earnings were no more than $86.
3. A savings account balance is now less than $550.
4. The number of club members is at least 25.
5. The spring calf class at the cattle show is for calves that weigh 825 pounds or less.
6. The minimum deposit for a new checking account is $75.

13. 7. a < 8
8. d ≤ 4
9. b ≥ 11  

14. Watch this short video on writing inequalities from a number line.

15. Write the inequality for each graph.

17. End of today’s lesson

18. Finding Possible Solutions for Inequalities
Since an inequality uses greater than or less than symbols, one variable inequalities have infinitely many solutions.
For example, any rational number greater than 4 will make the inequality x˃4 true.

19. List 3 possible solutions for each inequality.
k ˂ -7
z ≤ 14
m ≤ 2 3/5
f ˃ 0.24
n ≥ 23
p ˃ 16

20. Of the numbers 5, 6, or 7, which is a solution of the inequality f + 4 < 10?
To find which numbers are a solution, replace the variable with each of the numbers.
5 +4 ˂ 10
6 +4 ˂ 10
7 +4 ˂ 10
Which numbers are a solution?

21. Determine which number is a solution of the inequality.
Is the given value a solution of the inequality?
4. y – 3 < 5, y = 9
s ≥ 22, s = 8
6. r – 5 > 6, y = 10

22. Determine which number is a solution of the inequality.
– x ≤ 19; 3, 4, 5
r ≥ 18; 11, 10, 9
– h > 2; 6, 7, 8
– n ≤ 17; 13, 14, 15
j ≥ 29; 13, 12, 11
– f < 7; 2, 3, 4
q < 56; 5, 4, 3

23. Is the given value a solution of the inequality?
s ≥ 10; s = 7
– r < 9; r = 6
11. j – 11 ≥ 20; j = 32
12. t + 6 > 40; t = 35
m > 40; m = 16
x ≥ 80; x = 9
≤ 3z; z = 4
n > 26; n = 5