College Algebra
1st Edition
ISBN: 9781938168383
Author: Jay Abramson
Publisher: OpenStax
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![## Written Exercise 1
1. **Given that U is a universal set that contains all whole numbers less than 10 and A and B are subsets of U. Suppose:**
- A = {all factors of 18}
- B = {natural numbers greater than 2 but less than 8}
- C = {multiples of 2 less than 9}
a) **List the elements of U, A, B, and C.**
b) **Represent U, A, B, and C on a Venn diagram.**
c) **Find B ∪ C and A ∩ (B ∪ C)**
d) **Find (A ∩ B) ∪ (A ∩ C)**
e) **What can you say about A ∩ (B ∪ C) and (A ∩ B) ∪ (A ∩ C)?**
f) **Find A ∪ B and A ∪ C**
g) **Find (A ∪ B) ∩ (A ∪ C)**
h) **What can you say about A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)?**
2. **Solve and graph each of the following inequalities.**
a) 2x - 5 < 11 and 3x + 2 ≤ 20
b) x² - x - 6 > 0
c) 3m - 2(2m - 7) ≤ 2(3m + 4)
d) 3y - [7 + (2 - y)] ≥ y + 8
3. **Solve each absolute value inequality and graph the solution set where possible.**
a) 5x - 6 - 7 ≥ 2
b) 6 - 2x - 6 > 4
4. **Solve and graph \(\frac{3}{x + 1} - \frac{2}{x + 3} ≥ 1\)**
5. **Solve and graph 3x + 5 = 4**
6. **In the problems below, what value of x does each hold?**
a) x ⋅ 2 = 2x ⋅ 7
b) 3x + 5](https://content.bartleby.com/qna-images/question/ce2d9b9f-9b5b-48c6-9af0-1725d6f7a494/63f1d6fc-5bb6-4d13-9225-a4d6584ed6ef/z6mpmzb_processed.jpeg)
Transcribed Image Text:## Written Exercise 1
1. **Given that U is a universal set that contains all whole numbers less than 10 and A and B are subsets of U. Suppose:**
- A = {all factors of 18}
- B = {natural numbers greater than 2 but less than 8}
- C = {multiples of 2 less than 9}
a) **List the elements of U, A, B, and C.**
b) **Represent U, A, B, and C on a Venn diagram.**
c) **Find B ∪ C and A ∩ (B ∪ C)**
d) **Find (A ∩ B) ∪ (A ∩ C)**
e) **What can you say about A ∩ (B ∪ C) and (A ∩ B) ∪ (A ∩ C)?**
f) **Find A ∪ B and A ∪ C**
g) **Find (A ∪ B) ∩ (A ∪ C)**
h) **What can you say about A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)?**
2. **Solve and graph each of the following inequalities.**
a) 2x - 5 < 11 and 3x + 2 ≤ 20
b) x² - x - 6 > 0
c) 3m - 2(2m - 7) ≤ 2(3m + 4)
d) 3y - [7 + (2 - y)] ≥ y + 8
3. **Solve each absolute value inequality and graph the solution set where possible.**
a) 5x - 6 - 7 ≥ 2
b) 6 - 2x - 6 > 4
4. **Solve and graph \(\frac{3}{x + 1} - \frac{2}{x + 3} ≥ 1\)**
5. **Solve and graph 3x + 5 = 4**
6. **In the problems below, what value of x does each hold?**
a) x ⋅ 2 = 2x ⋅ 7
b) 3x + 5
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