Name



LESSON 6.4 Solving compound inequalities

Vocabulary:

A compound inequality. Consists of two separate inequalities joined by and or or.

EXAMPLE 1

Write and graph a compound inequality_______________________________

Translate the verbal phrases into an inequality. Then graph the inequality.

a. All real numbers that are less than or equal to 7 or greater than or equal to 10.

Inequality: x ≤ 7 or x ≥ 10 Interval Notation: [pic]

b. All real numbers that are greater than –1 and less than or equal to 1.

Inequality: –1 < x < 1 Interval Notation: [pic]

Exercises for Example 1

Translate the verbal phrases into an inequality, write it in Interval Notation and then graph the inequality.

|Phrase |Inequality |Interval Notation |Graph |

|All real numbers that are less than –3 or | | | |

|greater than 0. | | | |

|All real numbers that are less than 9 and | | | |

|greater than or equal to 7. | | | |

|All real numbers that are greater than or | | | |

|equal to 14 or less than or equal to 10. | | | |

EXAMPLE 2

Solve a compound inequality with ‘AND’

Solve 7 ≤ x – 4 ≤ 12. Graph your solution.

Solution

|7 ≤ x – 4 ≤ 12 |Write original inequality. | |

|7 ≤ x – 4 ≤ 12 |Add 4 to each expression. | |

|+4 +4 +4 | | |

|11 ≤ x ≤ 16 |Simplify. |[pic] |

EXAMPLE 3

Solve a compound inequality with ‘OR’

Solve 3x + 4 < 16 or 5x – 12 > 13. Graph your solution.

Solution

Solve the two inequalities separately.

|3x + 4 < 16 |or |5x – 12 > 13 |Write original inequality |

|3x + 4 – 4 < 16 – 4 |or |5x – 12 + 12 > 13 + 12 |Use addition or subtraction property of |

| | | |inequality |

|3x < 12 |or |5x > 25 |Simplify |

| |or | |Use division property of inequality |

|x < 4 |or |x > 5 |Simplify. |

The solutions are all real numbers less than 4 or greater than 5.

[pic]

Exercises for Examples 2 and 3_______________________________________

Solve the inequality. Write the Answer in Interval Notation. Graph your solution.

1. 9 < 2x + 3 < 15 2. 30 ≥ –7x – 12 > 16

3. 28 ≤ 4(2x – 3) ≤ 68 4. 3x – 7 < 11 or –x + 4 < -15

5. x + 18> 6 or 7x + 5 < –51 6. 3x + 8 > 7x – 12 or 9(x – 2) > 8x – 9

6.4 Solving Compound Inequalities: Class Examples

Solve the Inequality. Write your answer in Interval Notation. Graph your solution.

1. [pic] 2. [pic]

3. [pic] 4. [pic]

5. [pic] 6. [pic]

7. [pic] 8. [pic]

6.4 Homework

Translate the verbal phrase into an inequality. Then graph the inequality. Write the inequality in interval notation.

1. All real numbers that are less than or equal to -8 or greater than 12.

Inequality:___________________ Interval Notation:_____________________

2. All real numbers that are greater than or equal to [pic]and less than or equal to 10.

Inequality:___________________ Interval Notation:________________________

Write and graph an inequality that describes the situation. Write the inequality in set notation and interval notation.

3. The temperature inside a room is uncomfortable if the temperature is lower than [pic]F or higher than [pic]F.

Inequality:___________________ Interval Notation:_____________________

4. The minimum speed on the highway is 40 miles per hour, and the maximum speed is 60 miles per hour.

Inequality:___________________ Interval Notation:_____________________

Solve the inequality. Graph your solution and write it in set and interval notation.

5. [pic] Interval Notation:_____________________

6. [pic] Interval Notation:_____________________

7. [pic] Interval Notation:_____________________

8. [pic] or [pic] Interval Notation:_____________________

9. [pic] or [pic] Interval Notation:_____________________

10. [pic] or [pic] Interval Notation:_____________________

-----------------------

x

3

3

38

37

<

3

12

x

5

5x

>

ᦴᦻ吀呐呑呓呔呫呬呭呮呴咛咦咧咩咫咮咰咱哈哉쯯돯쮜路珯曯N̮䩪曏੐Ĉ栕殟?栖㽅1࠵䎁ᡊ伀J儀J唀Ĉࡖ愁ᡊᘙ䕨ㄿ㔀脈䩃䩏䩑䩡̳jᔀ齨鵫ᘀ䕨ㄿ㔀脈䩃䩏䩑ࡕ愁ᡊ洀H渄H甄Ĉᔜ齨鵫ᘀ䕨ㄿ䌀ᡊ伀J儀J愀ᡊ̬øᔀ齨鵫ᘀ䕨ㄿ㔀脈䩃䡅￶䩏䩑ࡕ愁ᡊ̮흪曎੐Ĉ栕殟?栖㽅1࠵䎁ᡊ伀J儀J唀Ĉࡖ愁ᡊ̨jᔀ齨鵫ᘀ䕨ㄿ㔀脈䩃䩏

5

25

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download