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ᡊ̬øᔀ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.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- company name and stock symbol
- why your name is important
- native american name generator
- why is my name important
- why is god s name important
- last name that means hope
- name for significant other
- name synonym list
- me and name or name and i
- name and i vs name and me
- name and i or name and myself
- name and i or name and me