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Prealgebra and Introductory Algebra

Richard N. Aufmann, Joanne S. Lockwood

Chapter 14

Inequalities - all with Video Answers

Educators


Section 1

Sets

00:39

Problem 1

The set $\{1,2,3\}$ is written using the ___ method. The set $\{x | x<4, x \in \text { positive integers }\}$ is written using ___ notation. The set $[-3,2]$ is written in ___ notation.

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00:40

Problem 2

Explain how to find a. the union of two sets and b. the intersection of two sets.

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00:31

Problem 3

Use the roster method to write the set.
The integers between 15 and 22

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00:26

Problem 4

Use the roster method to write the set.
The integers between $-10$ and $-4$

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00:30

Problem 5

Use the roster method to write the set.
The odd integers between 8 and 18

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00:35

Problem 6

Use the roster method to write the set.
$$\text { The even integers between }-11 \text { and }-1$$

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00:43

Problem 7

Find $A \cup B$.
$$A=\{3,4,5\} ; B=\{4,5,6\}$$

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00:34

Problem 8

Find $A \cup B$.
$$A=\{-3,-2,-1\} ; B=\{-2,-1,0\}$$

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00:33

Problem 9

Find $A \cup B$.
$$A=\{-10,-9,-8\} ; B=\{8,9,10\}$$

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00:52

Problem 10

Find $A \cup B$.
$$A=\{\mathrm{m}, \mathrm{n}, \mathrm{p}, \mathrm{q}\} ; B=\{\mathrm{m}, \mathrm{n}, \mathrm{o}\}$$

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00:42

Problem 11

Find $A \cup B$.
$$A=\{1,3,7,9\} ; B=\{7,9,11,13\}$$

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00:33

Problem 12

Find $A \cup B$.
$$A=\{-3,-2,-1\} ; B=\{-1,1,2\}$$

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00:26

Problem 13

Find $A \cap B$.
$$A=\{3,4,5\} ; B=\{4,5,6\}$$

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00:20

Problem 14

Find $A \cap B$.
$$A=\{-4,-3,-2\} ; B=\{-6,-5,-4\}$$

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00:33

Problem 15

Find $A \cap B$.
$$A=\{-4,-3,-2\} ; B=\{2,3,4\}$$

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00:32

Problem 16

Find $A \cap B$.
$$A=\{1,2,3,4\} ; B=\{1,2,3,4\}$$

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00:37

Problem 17

Find $A \cap B$.
$$A=\{a, b, c, d, e\} ; B=\{c, d, e, f, g\}$$

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00:33

Problem 18

Find $A \cap B$.
$$A=\{\mathrm{m}, \mathrm{n}, \mathrm{o}, \mathrm{p}\} ; B=\{\mathrm{k}, 1, \mathrm{m}, \mathrm{n}\}$$

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01:30

Problem 19

Use set-builder notation to write the set.
The negative integers greater than $-5$

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00:50

Problem 20

Use set-builder notation to write the set.
The positive integers less than 5

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00:26

Problem 21

Use set-builder notation to write the set.
The integers greater than 30

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00:27

Problem 22

Use set-builder notation to write the set.
The integers less than $-70$

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00:17

Problem 23

Use set-builder notation to write the set.
The real numbers greater than 8

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00:18

Problem 24

Use set-builder notation to write the set.
The real numbers less than 57

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00:34

Problem 25

Write the set in interval notation.
$$\{x | 1<x<2\}$$

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00:39

Problem 26

Write the set in interval notation.
$$\{x |-2<x \leq 4\}$$

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00:24

Problem 27

Write the set in interval notation.
$$\{x | x>3\}$$

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00:35

Problem 28

Write the set in interval notation.
$$\{x | x \leq 0\}$$

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00:39

Problem 29

Write the set in interval notation.
$$\{x |-4 \leq x<5\}$$

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00:21

Problem 30

Write the set in interval notation.
$$\{x |-3 \leq x \leq 0\}$$

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00:32

Problem 31

Write the set in interval notation.
$$\{x | x \leq 2\}$$

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00:39

Problem 32

Write the set in interval notation.
$$\{x | x \geq-3\}$$

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00:24

Problem 33

Write the set in interval notation.
$$\{x |-3 \leq x \leq 1\}$$

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00:25

Problem 34

Write the interval in sel-builder notation
$$[-4,5]$$

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00:26

Problem 35

Write the interval in sel-builder notation
$$(-5,-3)$$

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00:25

Problem 36

Write the interval in sel-builder notation
$$(4, \infty)$$

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00:29

Problem 37

Write the interval in sel-builder notation
$$(-\infty,-2]$$

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00:28

Problem 38

Write the interval in sel-builder notation
$$(4,9]$$

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00:31

Problem 39

Write the interval in sel-builder notation
$$[-3,-2]$$

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00:30

Problem 40

Write the interval in sel-builder notation
$$[0, \infty)$$

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00:26

Problem 41

Write the interval in sel-builder notation
$$(-\infty, 6]$$

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00:22

Problem 42

Write the interval in sel-builder notation
$$(-\infty, \infty)$$

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00:16

Problem 43

Graph the set.
(GRAPH CANNOT COPY)
$$[-5,4]$$

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00:17

Problem 44

Graph the set.
(GRAPH CANNOT COPY)
$$(-3,5]$$

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00:18

Problem 45

Graph the set.
(GRAPH CANNOT COPY)
$$\{x | x<4\}$$

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00:23

Problem 46

Graph the set.
(GRAPH CANNOT COPY)
$$\{x | x \geq-3\}$$

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00:24

Problem 47

Graph the set.
(GRAPH CANNOT COPY)
$$\{x | x \leq-4\}$$

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00:18

Problem 48

Graph the set.
(GRAPH CANNOT COPY)
$$\{x | x>0\}$$

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00:19

Problem 49

Graph the set.
(GRAPH CANNOT COPY)
$$(-\infty, 3]$$

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00:16

Problem 50

Graph the set.
(GRAPH CANNOT COPY)
$$(4, \infty)$$

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00:13

Problem 51

Graph the set.
(GRAPH CANNOT COPY)
$$[-1,3)$$

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00:16

Problem 52

Graph the set.
(GRAPH CANNOT COPY)
$$(-3,0]$$

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00:26

Problem 53

Graph the set.
(GRAPH CANNOT COPY)
$$\{x |-3<x<3\}$$

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00:29

Problem 54

Graph the set.
(GRAPH CANNOT COPY)
$$\{x | 0 \leq x<4\}$$

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00:20

Problem 55

Graph the set.
(GRAPH CANNOT COPY)
$$\{x | 2 \leq x \leq 4\}$$

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00:19

Problem 56

Graph the set.
(GRAPH CANNOT COPY)
$$\{x |-4<x<1\}$$

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00:24

Problem 57

Graph the set.
(GRAPH CANNOT COPY)
$$\{x |-\infty<x<\infty\}$$

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00:08

Problem 58

Graph the set.
(GRAPH CANNOT COPY)
$$(-\infty, \infty)$$

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00:23

Problem 59

How many elements are in the set given in interval notation as $(4,4) ?$

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00:21

Problem 60

How many elements are in the set given by $\{x | 4 \leq x \leq 4\} ?$

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00:38

Problem 61

To avoid shipping charges, one must spend a minimum $m$ of $\$ 250$.

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00:24

Problem 62

The temperature $t$ never got above freezing $\left(32^{\circ} \mathrm{F}\right)$.

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01:32

Problem 63

True or false? If $A \cup B=A,$ then $A \cap B=B$.

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00:50

Problem 64

Make up sets $A$ and $B$ such that $A \cup B$ has three elements and $A \cap B$ has no elements. Write your sets using the roster method.

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00:48

Problem 65

Make up sets $A$ and $B$ such that $A \cup B$ has four elements and $A \cap B$ has four elements. Write your sets using the roster method.

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01:28

Problem 66

Make up sets $A$ and $B$ such that $A \cup B$ has five elements and $A \cap B$ has two elements. Write your sets using the roster method.

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