1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Graph each number on the number line.
Warm Up
Graph each number on the number line. 2 3 4 5 6 7 8 1 9 10

3. Problem of the Day
Randy purchased a laser tag admission ticket for $5. Each time he plays, he pays an additional $1.50. Write an equation to find out how many games he can play if he has $20 to spend.
x = 20; Randy can play 10 games.

4. Sunshine State Standards
MA.6.A.3.2 Write, solve, and graph one- …step…inequalities.

5. Vocabulary
inequality
solution of an inequality

6. < > ≤ ≥ ≠ An inequality is a statement that two
quantities are not equal. The quantities
are compared by using one of the following
symbols:
< > ≤ ≥ ≠
An inequality may contain a variable, as in
x > 3. A solution of an equality is any value
of the variable that makes the statement true.

7. Additional Example 1: Graphing Inequalities
Graph the solutions of each inequality on a number line.
Draw an empty circle at 4to show that 4 is not a solution. Shade to the right to show that values greater than 4 are solutions.
A. t > 1
B. y  11
Draw a solid circle at 11 to
show that 11 is a solution.
Shade to the left to show
values that are equal to or
less than 11are also
solutions.

8. Graph the solution of the inequality b ≤ 4 on a number line.
Check It Out: Example 1
Graph the solution of the inequality b ≤ 4 on a number line.

9. Solve and graph each inequality.
Additional Example 2: Solving Inequalities with Addition or Subtraction
Solve and graph each inequality.
x – 3 ≥ 5
x – 3 ≥ 5
3 is subtracted from x.
Add 3 to both sides of the
inequality to undo the subtraction.
x ≥ 8 5 6 7 8 9 10 11 4 3 2 1 –
The solid circle at 8 shows that 8 is a solution.

10. Solve and graph each inequality.
Check It Out: Example 2
Solve and graph each inequality.
5 < x + 3 7 6 5 4 3 2 1
5 < x + 3 -3
- 3 2
< x or
x > 2

11. Solve and graph each inequality.
Additional Example 3: Solving Inequalities with Multiplication or Division
Solve and graph each inequality.
8z < 32
8z < 32
8 is multiplied by z.
8 8
Divide both sides of the
inequality by 8 to undo the
multiplication.
z < 4 5 6 7 8 9 10 11 4 3 2 1 –
The empty circle at 4 shows that 4 is not a solution.

12. Graph the solution of the inequality on a number line.
Check It Out: Example 3
Graph the solution of the inequality on a number line. a 4
> 4 a 4
4 ∙ > 4 ∙ 4
a  16

13. Additional Example 4: Write an Inequality to Represent the Situation
Six friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend.
Let m represent the amount the friends want to spend. 6
times
money need
should be less than or equal to
150 6 x m ≤
150
The inequality 6m ≤ 150 represents the situation.

14. Additional Example 4A Continued
Solve the inequality. 6m ≤ 150.
6m ≤
Divide both sides by 6 to undo
the multiplication. 6 6
m ≤ 25
Each friend can spend up to $25.

15. Additional Example 4 Continued
Six friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend.
Check Substitute the input value into the rule.
6(25) ≤ 150 = 150 ≤ 150
check
6(20) ≤ 150 = 120 ≤ 150
check

16. Derek must log at least 13 more hours of flight time.
Check It Out: Example 4
Derek must log at least 20 hours of flight time for a sport pilot certificate. So far, he has logged 7 hours. Write and solve an inequality to describe how much more flight time Derek needs to log.
7 + h > 20 -7 -7
h > 13
Derek must log at least 13 more hours of flight time.

17. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 17 17

18. 1. Graph the inequality x > 12 on the number line.
Lesson Quiz
1. Graph the inequality x > 12 on the number line.
Solve and graph each inequality.
x < 6
3. 
x < 2
–3 –2 –
y ≥ 32

19. Lesson Quiz for Student Response Systems
1. Identify the inequality.
A. x < 1
B. x < 1
C. x > 1
D. x > 1 19 19

20. Lesson Quiz for Student Response Systems
2. Solve the inequality x + 3 < 9.
A. x < 6
B. x < 12
C. x > 6
D. x > 12 20 20

21. Lesson Quiz for Student Response Systems
3. Solve the inequality
A. m < 5
B. m < 5
C. m > 36
D. m > 36 21 21