1. Use variables and appropriate operations to write inequality.
Inequalities
Use variables and appropriate operations to write inequality.

3. Preview
Warm Up
California Standards
Lesson Presentation

4. Warm Up Order each set of integers from least to greatest.
1. –7, 8, –9
2. –2, 2, 0, -1
3. –11, -13, -10
Write an algebraic expression for each word phrase.
4. 2 less than g
5. 5 minus the product of 3 and m
6. 1 more than the quotient of x and 4
–9, –7, 8
–2, –1, 0, 2
–13, –11, –10
g – 2
5 – 3m
x 4
1 +

5. AF1.1 Use variables and appropriate operators to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
California
Standards

6. Vocabulary
inequality
algebraic inequality
solution set

7. Inequality Symbols < less than > greater than
Notice open circles

8. Inequality Symbols ≤ less than or equal to ≥ greater than or equal to
Notice colored in circles

9. Symbol Meaning Word Phrases
An inequality compares two expressions using <, >, , or .
Symbol
Meaning
Word Phrases
<
> ≤ ≥
is less than
Fewer than, below
is greater than
More than, above
is less than or equal to
At most, no more than
is greater than or equal to
At least, no less than
An inequality that contains a variable is an algebraic inequality.

10. Additional Example 1: Translating Word Phrases into Inequalities
Write an inequality for each situation.
A. There are at least 35 people in the gym.
Let p = the number of people in the gym.
p ≥ 35
“At least” means greater than or equal to.
B. The carton holds at most 12 eggs.
Let e = the number of eggs the carton hold.
e ≤ 12
“At most” means less than or equal to.

11. Check It Out! Example 1
Write an inequality for each situation.
A. There are at most 10 gallons of gas in the tank.
Let g = the number of gallons of gas.
g ≤ 10
“At most” means less than or equal to.
B. There are fewer than 10 yards of fabric left.
Let y = the yards of fabric.
y < 10
“Fewer than” means less than.

12. Additional Example 2: Writing Inequalities
Write an inequality for each statement.
A. A number m multiplied by 5 is less than 25.
A number m multiplied by is less than 25.
m  <
5m < 25
B. The sum of a number y and 16 is no more than 100.
The sum of a number y and 16 is no more than 100
y ≤
y + 16 ≤ 100

13. Check It Out! Example 2
Write an inequality for each statement.
A. A number y plus 14 is greater than 21.
A number y plus is greater than 21.
y >
y + 14 > 21
B. A number t increased by 7 is more than 11
A number t is increased by is more than 11
t >
t + 7 > 11

14. A solution of an inequality is any value of the variable that makes the inequality true. All of the solutions of an inequality are called the solution set.
You can graph the solution set on a number line. The symbols < and > indicate an open circle.

15. a > 5 b ≤ 3 This open circle shows that 5 is not a solution.
The symbols ≤ and ≥ indicate a closed circle.
This closed circle shows that 3 is a solution.
b ≤ 3

16. Additional Example 3: Graphing Inequalities
Graph each inequality.
A. –1 > y
Draw an open circle at –1. The solutions are all values of y less than –1, so shade the line to the left of –1.
–3 –2 – 12
B. z ≥ –2
Draw a closed circle
at –2 and all values of z greater than So shade to the right of –2 .
1 2
–3 –2 –

17. Check It Out! Example 3 Graph each inequality. A. n < 3
Draw an open circle at 3. The solutions are all values of n less than 3, so shade the line to the left of 3.
–3 –2 –
B. a ≥ –4
Draw a closed circle
at –4. The solutions are all values greater than –4, so shade to the right of –4.
–6 –4 –

18. A compound inequality is the result of combining two inequalities
A compound inequality is the result of combining two inequalities. The words and and or are used to describe how the two parts are related.
The compound inequality –2 < y and y < 4 can be written as –2 < y < 4.
Writing Math

20. Additional Example 4: Writing Compound Inequalities
Write a compound inequality for each statement.
A. A number x is both less than 4 and greater than or equal to –2.5.
–2.5 ≤ x < 4
B. A number t is either greater than –1 or less than or equal to –7.
t > –1 or t ≤ –7

21. Check It Out! Example 4
Write a compound inequality for each statement.
A. A number t is both greater than 9 and less than or equal to 18.5
9 < t  18.5
B. A number y is either greater than –5 or less than or equal to –1.
y > –5 or y ≤ –1

22. Lesson Quiz: Part I
Write an inequality for each situation.
1. Fewer than 150 people bought tickets.
2. There are at least 20 finches in the cage.
Write an inequality for each statement.
3. A number n decreased by 5 is at most 16.
4. The product of 15 and a number z is greater than 100.
p < 150
f ≥ 20
n – 5 ≤ 16
15z > 100

23. º Lesson Quiz: Part II Graph each inequality. 5. m ≤ 1 6. –3 < y –1 2 3
6. –3 < y 1 2 3 –1 –2 –