Unit 5 Worksheet 2



Algebra 1

7.2 Compound Inequalities

NOTES

Recall:

Write, in words, what each inequality says. Start with the variable first in your sentence. Then, write 3 values for x that are solutions for each inequality.

a. x > 5 b. x < -2

Solutions: Solutions:

c. 3 > x d. -1 < x

Solutions: Solutions:

Compound Inequality: Two or more inequalities that are connected by the words ______

or ______ .

Intersection of Inequalities: A compound inequality that contains the word _________.

**This type of compound inequality is true if both inequalities are true.

Ex: x > 6 and x < 9 can be combined together and written as

Ex: The ages of the students in this class are greater than 12 but less than 16.

Union of Inequalities: A compound inequality that contains the word _____.

**This type of compound inequality is true if at least one of the inequalities is true.

Ex: x > 2 or x < -1 cannot be combined together into one inequality.

Ex: The low/high temperature each day in November was either less than 40        degrees or greater than 65 degrees.

Examples:

Rewrite each compound inequality as two separate inequalities. Then graph on the number line provided. Write 3 solutions for each inequality.

a. -6 < x < 1 b. 0 < x < 4

Solutions: Solutions:

Graph each compound inequality. Write 3 solutions for each inequality.

c. x < 1 or x > 5 d. x < -2 or x > 3

Solutions: Solutions:

Solve each compound inequality. Then graph. Write 3 solutions for each inequality.

e. -2 < x + 5 < 4 f. x – 4 < -6 or -3x < -12

Solutions: Solutions:

Solve each compound inequality. Then graph. Write 3 solutions for each inequality.

g. 6 < 2(x – 1) < 10 h. 3x + 2 < -10 or -x – 1 < 1

Solutions: Solutions:

Name:__________________________ Period:_____________

7.2 ASSIGNMENT: Level C

|Rewrite each compound inequality as two separate inequalities. Then graph. Write 3 solutions for each. |

|1. -2 < x < 5 |2. -5 < x < 3 |3. 1 < x < 6 |

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|Solutions: |Solutions: |Solutions: |

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|Graph each compound inequality. Write 3 solutions for each. |

|4. x < -1 or x > 5 |5. x < 0 or x > 6 |6. x > -1 or x < -5 |

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|Solutions: |Solutions: |Solutions: |

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| Level B |

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|Solve each inequality. Then, rewrite each inequality as two separate inequalities and graph. |

|7. 1 < x + 3 < 5 |8. –2 ( x – 4 < 1 |9. x + 1 < 3 or -2x < -10 |

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|Solutions: |Solutions: |Solutions: |

Level A

|10. 3 < 2x + 1 < 7 |11. 3x – 4 < 5 or 2x – 6 > 6 |12. –5 < 3 – 2x < 11 |

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|Solutions: |Solutions: |Solutions: |

|Write an inequality which describes each graph. |

|13. |14. |

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|15. |16. |

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|Write a compound inequality that represents each problem. Then solve each problem and write 3 possible solutions for each. |

|17. Most snakes must live in places where temperatures range between 75 to |18. The cost of cell phones are either less than $60 or more than $110. |

|90 degrees. | |

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PRACTICE TEST

|Level C |Level B |Level A |

|2C. Graph the compound inequality. |2B. Solve the compound inequality and graph. |2A. Use the compound inequality to answer the |

| | |questions below. |

|[pic] or [pic] |-1 < x + 4 < 6 |              |

| | |-15 < 4x – 7 < 17 |

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| | |a) Solve the compound inequality. |

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| | |b) Graph the solution. |

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| | |c) Write 3 solutions for the inequality. |

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ANSWERS:

|1. x > -2 and x < 5 |2. x > -5 and x < 3 |3. x > 1 and x < 6 |

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|Solutions: Answers will vary |Solutions: Answers will vary |Solutions: Answers will vary |

|”Choose any numbers greater than -2 and less than |”Choose any numbers greater than -5 and less than |”Choose any numbers greater than or equal to 1 and |

|5” |or equal to 3” |less than or equal to 6” |

|4. x < -1 or x > 5 |5. x < 0 or x > 6 |6. x > -1 or x < -5 |

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|Solutions: Answers will vary |Solutions: Answers will vary |Solutions: Answers will vary |

|”Choose any numbers less than -1 or greater than 5”|”Choose any numbers less than or equal to 0 or |”Choose any numbers less than or equal to -5 or |

| |greater than 6” |greater than -1” |

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|7. -2 < x < 2 |8. 2 < x < 5 |9. x < 2 or x > 5 |

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|x > -2 and x < 2 |x > 2 and x < 5 | |

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| |Solutions: Answers will vary |Solutions: Answers will vary |

|Solutions: Answers will vary |”Choose any numbers greater than or equal to 2 and |”Choose any numbers less than 2 or greater than 5” |

|”Choose any numbers greater than -2 and less than |less than 5” | |

|2” | | |

|10. 1 < x < 3 |11. x < 3 or x > 6 |12. 4 > x > -4 |

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|x > 1 and x < 3 | |x > -4 and x < 4 |

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|Solutions: Answers will vary |Solutions: Answers will vary |Solutions: Answers will vary |

|”Choose any numbers greater than 1 and less than 3”|”Choose any numbers less than or equal to 3 or |”Choose any numbers greater than -4 and less than |

| |greater than 6” |or equal to 4” |

|13. -4 < x < 5 |14. x < -3 or x > 4 |

|15. x < -1 or x > 0 |16. -5 < x < 1 |

|17. 75˚ < temp < 90˚ |18. Cost < $60 or Cost > $110 |

|Practice Test | | |

|1C [pic] |1B [pic] |1A a) [pic] |

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| | |c) Answers vary |

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