Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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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
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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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