Warm-Up6.2

Solve and graph the inequalities:

1. 2x +10 > 7(x + 1) 2. 73x

21

x > -85

3x

Objectives:1. Solve compound inequalities2. Set up and solve real-life linear

inequalities

 

Vocabulary: compound inequalities, “and,” “or”

Solving Compound Inequalities6.3

Vocabulary: compound inequality – two inequalities connected by “and” or “or”

and – must satisfy both conditions

The best math teachers are smart AND teach at OHS.

6.3Solving Compound Inequalities

Vocabulary: compound inequality – two inequalities connected by “and” or “or”

or – must satisfy at least one condition, but could be both

I want to learn from a math teacher that gives little homework OR is really funny.

6.3Solving Compound Inequalities

Write an inequality that represents the set of numbers and then graph it.

1. Numbers that are greater than 0 and less than or equal to 4.

2. Numbers that are greater than or equal to -2 and less than 3.

Example 1 Writing Compound Inequalities

0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1-4-5-6-7-8-9-10-11

0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1-4-5-6-7-8-9-10-11

x > 0 and x < 4

x > -2 and x < 3

0 < x < 4

-2 < x < 3

Write an inequality that represents the set of numbers and then graph it.

3. Numbers that are less than -1 or greater than 2.

4. Number that are less than or equal to -3 or greater than 0.

0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1-4-5-6-7-8-9-10-11

0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1-4-5-6-7-8-9-10-11

x < -1 or x > 2

Example 1 Writing Compound Inequalities

x < -3 or x > 0

Write an inequality that describes each condition.

1. Water is a non-liquid when the temperature is 32°F or below or at least 212°F.

2. A refrigerator is designed to work on an electric line carrying from 115 volts to 120 volts.

Example 2 Writing Compound Inequalities

t < 32 or t > 212

115 < v < 120

Solve the inequality and graph it.

1. -5 < 2x + 3 < 7

2. -2 < 3x – 8 < 10

Example 3 Solving a Compound Inequality with “And”

2 < x < 6

-4 < x < 2

0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1-4-5-6-7-8-9-10-11

0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1-4-5-6-7-8-9-10-11

Solve the inequality and graph it.

3. -2 < -2 – x < 1

4. -3 < -1 – 2x < 5

Example 3 Solving a Compound Inequality with “And”

-3 < x < 1

0 > x > -3or -3 < x < 0

0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1-4-5-6-7-8-9-10-11

0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1-4-5-6-7-8-9-10-11

Solve the inequality and graph it.

5. 3x + 1 < 4 or 2x – 5 > 7

6. 6x – 5 < 7 or 8x + 1 > 25

Example 4 Solving a Compound Inequality with “Or”

x < 2 or x > 3

x < 1 or x > 6

0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1-4-5-6-7-8-9-10-11

0 1 2 3 4 5 6 7 8 9 10 11-3 -2 -1-4-5-6-7-8-9-10-11

Daily Homework Quizpg. 349 #6-9 in textbook• Solve and graph

• Once you finish, begin on the homework assignment!

Algebra 1

To be completed for an in-class participation grade!

Tonight’s Homework:

pg. 349 #12-34 even (only 12 problems)

BRING YOUR BOOKS BRING YOUR BOOKS TOMORROW!TOMORROW!

Algebra 1