SECTION 1.1 Numbers
Chapter 1 Introductory Information and Review
Section 1.1: Numbers
Types of Numbers Order on a Number Line
Types of Numbers
Natural Numbers:
MATH 1300 Fundamentals of Mathematics 1
CHAPTER 1 Introductory Information and Review
Example:
Solution:
Even/Odd Natural Numbers:
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SECTION 1.1 Numbers
Whole Numbers:
Example:
Solution:
Integers:
MATH 1300 Fundamentals of Mathematics 3
CHAPTER 1 Introductory Information and Review
Example:
Solution:
Even/Odd Integers:
Example:
Solution:
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CHAPTER 1 Introductory Information and Review
Irrational Numbers:
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CHAPTER 1 Introductory Information and Review
Additional Example 1:
Solution:
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SECTION 1.1 Numbers
Additional Example 2:
Solution:
Natural Numbers:
Whole Numbers:
Integers:
Prime/Composite Numbers:
Positive/Negative Numbers:
MATH 1300 Fundamentals of Mathematics 9
CHAPTER 1 Introductory Information and Review
Even/Odd Numbers:
Rational Numbers:
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SECTION 1.1 Numbers
Additional Example 3:
Solution:
Natural Numbers:
Whole Numbers:
MATH 1300 Fundamentals of Mathematics 11
CHAPTER 1 Introductory Information and Review
Integers:
Prime/Composite Numbers:
Positive/Negative Numbers:
Even/Odd Numbers:
Rational Numbers:
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CHAPTER 1 Introductory Information and Review
Order on a Number Line
The Real Number Line:
Example:
Solution:
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SECTION 1.1 Numbers
Inequality Symbols:
The following table describes additional inequality symbols.
Example:
Solution:
MATH 1300 Fundamentals of Mathematics 17
CHAPTER 1 Introductory Information and Review
Example:
Solution:
Example:
Solution:
Additional Example 1:
Solution:
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CHAPTER 1 Introductory Information and Review
Additional Example 3:
Solution:
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Exercise Set 1.1: Numbers
State whether each of the following numbers is prime, composite, or neither. If composite, then list all the factors of the number.
1. (a) 8 (b) 5 (c) 1(d) (e) 12
2. (a) 11 (b) (c) 15(d) 0 (e)
Answer the following.
3. In (a)-(e), use long division to change the following fractions to decimals.
(a) (b) (c)
(d) (e) Note:
Notice the pattern above and use it as a shortcut in (f)-(m) to write the following fractions as decimals without performing long division.
(f) (g) (h)
(i) (j) (k)
(l) (m) Note:
4. Use the patterns from the problem above to change each of the following decimals to either a proper fraction or a mixed number.
(a) (b) (c)
(d) (e) (f)
State whether each of the following numbers is rational or irrational. If rational, then write the number as a ratio of two integers. (If the number is already written as a ratio of two integers, simply rewrite the number.)
5. (a) 0.7 (b) (c)
(d) (e) (f)
(g) 12 (h) (i)
(j) (k)
6. (a) (b) (c)
(d) (e) (f)
(g) 3.1 (h) (i) 0
(j) (k) 0.03003000300003…
Circle all of the words that can be used to describe each of the numbers below.
7.Even Odd Positive NegativePrime Composite Natural WholeInteger Rational Irrational RealUndefined
8.
Even Odd Positive NegativePrime Composite Natural WholeInteger Rational Irrational RealUndefined
9.
Even Odd Positive NegativePrime Composite Natural WholeInteger Rational Irrational RealUndefined
10.
Even Odd Positive NegativePrime Composite Natural WholeInteger Rational Irrational RealUndefined
Answer the following.
11. Which elements of the set
belong
to each category listed below?
(a) Even (b) Odd(c) Positive (d) Negative(e) Prime (f) Composite(g) Natural (h) Whole(i) Integer (j) Real(k) Rational (l) Irrational(m) Undefined
MATH 1300 Fundamentals of Mathematics 23
Exercise Set 1.1: Numbers
12. Which elements of the set
belong to each category listed below?
(a) Even (b) Odd(c) Positive (d) Negative(e) Prime (f) Composite(g) Natural (h) Whole(i) Integer (j) Real(k) Rational (l) Irrational(m) Undefined
Fill in each of the following tables. Use “Y” for yes if the row name applies to the number or “N” for no if it does not.
13. 55
UndefinedNaturalWholeIntegerRationalIrrationalPrimeCompositeReal
14.
2.36
UndefinedNaturalWholeIntegerRationalIrrationalPrimeCompositeReal
Answer the following. If no such number exists, state “Does not exist.”
15. Find a number that is both prime and even.
16. Find a rational number that is a composite number.
17. Find a rational number that is not a whole number.
18. Find a prime number that is negative.
19. Find a real number that is not a rational number.
20. Find a whole number that is not a natural number.
21. Find a negative integer that is not a rational number.
22. Find an integer that is not a whole number.
23. Find a prime number that is an irrational number.
24. Find a number that is both irrational and odd.
Answer True or False. If False, justify your answer.j
25. All natural numbers are integers.
26. No negative numbers are odd.
27. No irrational numbers are even.
28. Every even number is a composite number.
29. All whole numbers are natural numbers.
30. Zero is neither even nor odd.
31. All whole numbers are integers.
32. All integers are rational numbers.
33. All nonterminating decimals are irrational numbers.
34. Every terminating decimal is a rational number.
Answer the following.
35. List the prime numbers less than 10.
36. List the prime numbers between 20 and 30.
37. List the composite numbers between 7 and 19.
38. List the composite numbers between 31 and 41.
39. List the even numbers between and .
40. List the odd numbers between and .
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Exercise Set 1.1: Numbers
Fill in the appropriate symbol from the set .
41. ______
42. 3 ______
43. ______
44. ______
45. ______ 9
46. ______
47. 5.32______
48. ______
49. ______
50. ______
51. ______
52. ______
53. ______ 4
54. 7 ______
55. ______
56. ______ 5
Answer the following.
57. Find the additive inverse of the following numbers. If undefined, write “undefined.”(a) 3 (b) (c) 1(d) (e)
58. Find the multiplicative inverse of the following numbers. If undefined, write “undefined.”(a) 3 (b) (c) 1(d) (e)
59. Find the multiplicative inverse of the following numbers. If undefined, write “undefined.”(a) (b) (c)
(d) (e)
60. Find the additive inverse of the following numbers. If undefined, write “undefined.”(a) (b) (c)
(d) (e)
61. Place the correct number in each of the following blanks:(a) The sum of a number and its additive
inverse is _____. (Fill in the correct number.)
(b) The product of a number and its multiplicative inverse is _____. (Fill in the correct number.)
62. Another name for the multiplicative inverse is the ____________________.
Order the numbers in each set from least to greatest and plot them on a number line. (Hint: Use the approximations and
.)
63.
64.
MATH 1300 Fundamentals of Mathematics 25
CHAPTER 1 Introductory Information and Review
Section 1.2: Integers
Operations with Integers
Operations with Integers
Absolute Value:
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SECTION 1.2 Integers
Addition of Integers:
Example:
Solution:
Subtraction of Integers:
MATH 1300 Fundamentals of Mathematics 27
CHAPTER 1 Introductory Information and Review
Example:
Solution:
Multiplication of Integers:
Example:
Solution:
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SECTION 1.2 Integers
Division of Integers:
Example:
Solution:
MATH 1300 Fundamentals of Mathematics 29
CHAPTER 1 Introductory Information and Review
Additional Example 1:
Solution:
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CHAPTER 1 Introductory Information and Review
Additional Example 3:
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CHAPTER 1 Introductory Information and Review
Additional Example 4:
Solution:
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Exercise Set 1.2: Integers
Evaluate the following.
1. (a) (b) (c)(d) (e)
2. (a) (b) (c)(d) (e)
3. (a) (b) (c)(d)
4. (a) (b) (c)(d)
5. (a) (b) (c)(d) (e) (f)(g) (h)
6. (a) (b) (c)(d) (e) (f)(g) (f)
Fill in the appropriate symbol from the set .
7. (a) ____ 0 (b) ____ 0(c) ____ 0 (d) ____ 0
8. (a) ____ 0 (b) ____ 0(c) ____ 0 (d) ___ 0
Evaluate the following. If undefined, write “Undefined.”
9. (a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(j) (k) (l)
10. (a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(j) (k) (l)
11. (a) (b) (c)
(d) (e) (f)
12. (a) (b) (c)
(d) (e) (f)
13. (a) (b)(c)(d)
14. (a) (b)(c)(d)
15. (a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(j) (k) (l)
(m) (n) (o)
16. (a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(j) (k) (l)
(m) (n) (o)
MATH 1300 Fundamentals of Mathematics 35
CHAPTER 1 Introductory Information and Review
Section 1.3: Fractions
Greatest Common Divisor and Least Common Multiple Addition and Subtraction of Fractions Multiplication and Division of Fractions
Greatest Common Divisor and Least Common Multiple
Greatest Common Divisor:
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SECTION 1.3 Fractions
A Method for Finding the GCD:
Least Common Multiple:
MATH 1300 Fundamentals of Mathematics 37
CHAPTER 1 Introductory Information and Review
A Method for Finding the LCM:
Example:
Solution:
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SECTION 1.3 Fractions
The LCM is
Additional Example 1:
Solution:
MATH 1300 Fundamentals of Mathematics 39
CHAPTER 1 Introductory Information and Review
The LCM is .
Additional Example 2:
Solution:
The LCM is .
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SECTION 1.3 Fractions
Additional Example 3:
Solution:
The LCM is .
MATH 1300 Fundamentals of Mathematics 41
CHAPTER 1 Introductory Information and Review
Additional Example 4:
Solution:
The LCM is .
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SECTION 1.3 Fractions
Addition and Subtraction of Fractions
Addition and Subtraction of Fractions with Like Denominators:
and
Example:
Solution:
MATH 1300 Fundamentals of Mathematics 43
CHAPTER 1 Introductory Information and Review
Addition and Subtraction of Fractions with Unlike Denominators:
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SECTION 1.3 Fractions
Example:
Solution:
Additional Example 1:
MATH 1300 Fundamentals of Mathematics 45
CHAPTER 1 Introductory Information and Review
Solution:
Additional Example 2:
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CHAPTER 1 Introductory Information and Review
Solution:
(b) We must rewrite the given fractions so that they have a common denominator.Find the LCM of the denominators 14 and 21 to find the least common denominator.
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CHAPTER 1 Introductory Information and Review
Multiplication and Division of Fractions
Multiplication of Fractions:
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SECTION 1.3 Fractions
Example:
Solution:
Division of Fractions:
Example:
Solution:
MATH 1300 Fundamentals of Mathematics 51
CHAPTER 1 Introductory Information and Review
Additional Example 1:
Solution:
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CHAPTER 1 Introductory Information and Review
Additional Example 3:
Solution:
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Exercise Set 1.3: Fractions
For each of the following groups of numbers,(a) Find their GCD (greatest common divisor).(b) Find their LCM (least common multiple).
1. 6 and 8
2. 4 and 5
3. 7 and 10
4. 12 and 15
5. 14 and 28
6. 6 and 22
7. 8 and 20
8. 9 and 18
9. 18 and 30
10. 60 and 210
11. 16, 20, and 24
12. 15, 21, and 27
Change each of the following improper fractions to a mixed number.
13. (a) (b) (c)
14. (a) (b) (c)
15. (a) (b) (c)
16. (a) (b) (c)
Change each of the following mixed numbers to an improper fraction.
17. (a) (b) (c)
18. (a) (b) (c)
19. (a) (b) (c)
20. (a) (b) (c)
Evaluate the following. Write all answers in simplest form. (If the answer is a mixed number/improper fraction, then write the answer as a mixed number.)
21. (a) (b)
22. (a) (b)
23. (a) (b)
24. (a) (b)
25. (a) (b)
26. (a) (b)
27. (a) (b)
28. (a) (b)
Evaluate the following. Write all answers in simplest form. (If the answer is a mixed number/improper fraction, then write the answer as a mixed number.)
29. (a) (b)
30. (a) (b)
31. (a) (b)
32. (a) (b)
33. (a) (b)
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Exercise Set 1.3: Fractions
34. (a) (b)
35. (a) (b)
36. (a) (b)
37. (a) (b)
38. (a) (b)
39. (a) (b)
40. (a) (b)
Evaluate the following. Write all answers in simplest form. (If the answer is a mixed number/improper fraction, then write the answer as an improper fraction.)
41. (a) (b)
42. (a) (b)
43. (a) (b)
44. (a) (b)
Evaluate the following. Write all answers in simplest form. (If the answer is a mixed number/improper fraction, then write the answer as an improper fraction.)
45. (a) (b) (c)
46. (a) (b) (c)
47. (a) (b) (c)
48. (a) (b) (c)
49. (a) (b) (c)
50. (a) (b) (c)
51. (a) (b) (c)
52. (a) (b) (c)
Evaluate the following. Write all answers in simplest form. (If the answer is a mixed number/improper fraction, then write the answer as a mixed number.)
53. (a) (b)
54. (a) (b)
55. (a) (b)
56. (a) (b)
57. (a) (b)
58. (a) (b)
MATH 1300 Fundamentals of Mathematics 57
CHAPTER 1 Introductory Information and Review
Section 1.4: Exponents and Radicals
Evaluating Exponential Expressions Square Roots
Evaluating Exponential Expressions
Two Rules for Exponential Expressions:
Example:
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CHAPTER 1 Introductory Information and Review
Solution:
Example:
Solution:
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SECTION 1.4 Exponents and Radicals
Additional Properties for Exponential Expressions:
Two Definitions:
Quotient Rule for Exponential Expressions:
Exponential Expressions with Bases of Fractions:
Example:
Solution:
MATH 1300 Fundamentals of Mathematics 61
SECTION 1.4 Exponents and Radicals
Additional Example 1:
Solution:
MATH 1300 Fundamentals of Mathematics 63
CHAPTER 1 Introductory Information and Review
Additional Example 2:
Solution:
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SECTION 1.4 Exponents and Radicals
Additional Example 3:
Solution:
MATH 1300 Fundamentals of Mathematics 65
SECTION 1.4 Exponents and Radicals
Square Roots
Definitions:
Two Rules for Square Roots:
Writing Radical Expressions in Simplest Radical Form:
MATH 1300 Fundamentals of Mathematics 67
CHAPTER 1 Introductory Information and Review
Example:
Solution:
Example:
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SECTION 1.4 Exponents and Radicals
Solution:
Exponential Form:
Additional Example 1:
Solution:
MATH 1300 Fundamentals of Mathematics 69
CHAPTER 1 Introductory Information and Review
Additional Example 2:
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SECTION 1.4 Exponents and Radicals
Solution:
Additional Example 3:
Solution:
MATH 1300 Fundamentals of Mathematics 71
Exercise Set 1.4: Exponents and Radicals
Write each of the following products instead as a base and exponent. (For example, )
1. (a) (b)(c) (d)
2. (a) (b)(c) (d)
Fill in the appropriate symbol from the set .
3. ______ 0
4. ______ 0
5. ______ 0
6. ______ 0
7. ______
8. ______
Evaluate the following.
9. (a) (b) (c)(d) (e) (f)
(g) (h) (i)
(j) (k) (l)
(m) (n) (o)
10. (a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(j) (k) (l)
(m) (n) (o)
11. (a) (b) (c)
12. (a) (b) (c)
Write each of the following products instead as a base and exponent. (Do not evaluate; simply write the base and exponent.) No answers should contain negative exponents.
13. (a) (b)
14. (a) (b)
15. (a) (b)
16. (a) (b)
17. (a) (b)
18. (a) (b)
19. (a) (b)
20. (a) (b)
Rewrite each expression so that it contains positive exponent(s) rather than negative exponent(s), and then evaluate the expression.
21. (a) (b) (c)
22. (a) (b) (c)
23. (a) (b)
24. (a) (b)
25. (a) (b)
26. (a) (b)
27. (a) (b)
28. (a) (b)
MATH 1300 Fundamentals of Mathematics 73
Exercise Set 1.4: Exponents and Radicals
Evaluate the following.
29. (a) (b)
30. (a) (b)
31. (a) (b)
32. (a) (b)
Simplify the following. No answers should contain negative exponents.
33. (a) (b)
34. (a) (b)
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
Write each of the following expressions in simplest radical form or as a rational number (if appropriate). If it is already in simplest radical form, say so.
45. (a) (b) (c)
46. (a) (b) (c)
47. (a) (b) (c)
48. (a) (b) (c)
49. (a) (b) (c)
50. (a) (b) (c)
51. (a) (b) (c)
52. (a) (b) (c)
53. (a) (b) (c)
54. (a) (b) (c)
55. (a) (b) (c)
56. (a) (b) (c)
University of Houston Department of Mathematics74
Exercise Set 1.4: Exponents and Radicals
57. (a) (b)
58. (a) (b)
Evaluate the following.
59. (a) (b) (c)
60. (a) (b) (c)
We can evaluate radicals other than square roots. With square roots, we know, for example, that
, since , and is not a real number. (There is no real number that when squared gives a value of , since and give a value of 49, not . The answer is a complex number, which will not be addressed in this course.) In a similar fashion, we can compute the following:
Cube Roots, since .
, since .
Fourth Roots, since .
is not a real number.
Fifth Roots, since .
, since .
Sixth Roots
, since .
is not a real number.
Evaluate the following. If the answer is not a real number, state “Not a real number.”
61. (a) (b) (c)
62. (a) (b) (c)
63. (a) (b) (c)
64. (a) (b) (c)
65. (a) (b)
(c)
66. (a) (b) (c)
67. (a) (b) (c)
68. (a) (b) (c)
69. (a) (b)
(c)
70. (a) (b) (c)
MATH 1300 Fundamentals of Mathematics 75
CHAPTER 1 Introductory Information and Review
Section 1.5: Order of Operations
Evaluating Expressions Using the Order of Operations
Evaluating Expressions Using the Order of Operations
Rules for the Order of Operations:
1) Operations that are within parentheses and other grouping symbols are performedfirst. These operations are performed in the order established in the following steps.If grouping symbols are nested, evaluate the expression within the innermostgrouping symbol first and work outward.
2) Exponential expressions and roots are evaluated first.
3) Multiplication and division are performed next, moving left to right and performingthese operations in the order that they occur.
4) Addition and subtraction are performed last, moving left to right and performingthese operations in the order that they occur.
Upon removing all of the grouping symbols, repeat the steps 2 through 4 until thefinal result is obtained.
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SECTION 1.5 Order of Operations
Example:
Solution:
Example:
Solution:
Additional Example 1:
MATH 1300 Fundamentals of Mathematics 77
CHAPTER 1 Introductory Information and Review
Solution:
Additional Example 2:
Solution:
Additional Example 3:
Solution:
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SECTION 1.5 Order of Operations
Additional Example 4:
Solution:
Additional Example 5:
Solution:
MATH 1300 Fundamentals of Mathematics 79
Exercise Set 1.5: Order of Operations
Answer the following.
1. In the abbreviation PEMDAS used for order of operations,
(a) State what each letter stands for:P: ____________________E: ____________________M: ____________________D: ____________________A: ____________________S: ____________________
(b) If choosing between multiplication and division, which operation should come first? (Circle the correct answer.)
MultiplicationDivisionWhichever appears first
(c) If choosing between addition and subtraction, which operation should come first? (Circle the correct answer.)
AdditionSubtractionWhichever appears first
2. When performing order of operations, which of the following are to be viewed as if they were enclosed in parentheses? (Circle all that apply.)
Absolute value barsRadical symbolsFraction bars
Evaluate the following.
3. (a) (b)(c) (d)(e) (f)
4. (a) (b)(c) (d)(e) (f)
5. (a) (b)
(c) (d)
6. (a) (b)
(c) (d)
7. (a) (b)(c) (d)(e) (f)
8. (a) (b)(c) (d)(e) (f)
9. (a) (b)
(c) (d)
10. (a) (b)
(c) (d)
11. (a) (b)
(c) (d)
(e) (f)
12. (a) (b)
(c) (d)
(e) (f)
13. (a) (b)(c)
14. (a) (b)(c)
15. (a) (b)
(c)
16. (a) (b)
(c)
17. (a) (b) (c)
18. (a) (b) (c)
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Exercise Set 1.5: Order of Operations
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
MATH 1300 Fundamentals of Mathematics 81
Exercise Set 1.5: Order of Operations
Evaluate the following expressions for the given values of the variables.
47. for .
48. for .
49. for and .
50. for .
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SECTION 1.6 Solving Linear Equations
Section 1.6: Solving Linear Equations
Linear Equations
Linear Equations
Rules for Solving Equations:
Linear Equations:
Example:
MATH 1300 Fundamentals of Mathematics 83
CHAPTER 1 Introductory Information and Review
Solution:
Example:
Solution:
Additional Example 1:
Solution:
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SECTION 1.6 Solving Linear Equations
Additional Example 2:
Solution:
Additional Example 3:
Solution:
MATH 1300 Fundamentals of Mathematics 85
Exercise Set 1.6: Solving Linear Equations
Solve the following equations algebraically.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
University of Houston Department of Mathematics86
SECTION 1.7 Interval Notation and Linear Inequalities
Section 1.7: Interval Notation and Linear Inequalities
Linear Inequalities
Linear Inequalities
Rules for Solving Inequalities:
MATH 1300 Fundamentals of Mathematics 87
CHAPTER 1 Introductory Information and Review
Interval Notation:
Example:
Solution:
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SECTION 1.7 Interval Notation and Linear Inequalities
Example:
Solution:
Example:
MATH 1300 Fundamentals of Mathematics 89
CHAPTER 1 Introductory Information and Review
Solution:
Additional Example 1:
Solution:
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SECTION 1.7 Interval Notation and Linear Inequalities
Additional Example 2:
Solution:
MATH 1300 Fundamentals of Mathematics 91
CHAPTER 1 Introductory Information and Review
Additional Example 3:
Solution:
Additional Example 4:
Solution:
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SECTION 1.7 Interval Notation and Linear Inequalities
Additional Example 5:
Solution:
Additional Example 6:
Solution:
MATH 1300 Fundamentals of Mathematics 93
CHAPTER 1 Introductory Information and Review
Additional Example 7:
Solution:
University of Houston Department of Mathematics94
Exercise Set 1.7: Interval Notation and Linear Inequalities
For each of the following inequalities:(a) Write the inequality algebraically.(b) Graph the inequality on the real number line.(c) Write the inequality in interval notation.
1. x is greater than 5.
2. x is less than 4.
3. x is less than or equal to 3.
4. x is greater than or equal to 7.
5. x is not equal to 2.
6. x is not equal to .
7. x is less than
8. x is greater than .
9. x is greater than or equal to .
10. x is less than or equal to .
11. x is not equal to .
12. x is not equal to 3.
13. x is not equal to 2 and x is not equal to 7.
14. x is not equal to and x is not equal to 0.
Write each of the following inequalities in interval notation.
15.
16.
17.
18.
19.
20.
21.
22.
Write each of the following inequalities in interval notation.
23.
24.
25.
26.
27.
28.
Given the set , use substitution to
determine which of the elements of S satisfy each of the following inequalities.
29.
30.
31.
32.
33.
34.
For each of the following inequalities:(a) Solve the inequality.(b) Graph the solution on the real number line.(c) Write the solution in interval notation.
35.
MATH 1300 Fundamentals of Mathematics
95
Exercise Set 1.7: Interval Notation and Linear Inequalities
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
Which of the following inequalities can never be true?
59. (a)(b)
(c)(d)
60. (a)(b)(c)(d)
Answer the following.
61. You go on a business trip and rent a car for $75 per week plus 23 cents per mile. Your employer will pay a maximum of $100 per week for the rental. (Assume that the car rental company rounds to the nearest mile when computing the mileage cost.)
(a) Write an inequality that models this situation.
(b) What is the maximum number of miles that you can drive and still be reimbursed in full?
62. Joseph rents a catering hall to put on a dinner theatre. He pays $225 to rent the space, and pays an additional $7 per plate for each dinner served. He then sells tickets for $15 each.
(a) Joseph wants to make a profit. Write an inequality that models this situation.
(b) How many tickets must he sell to make a profit?
63. A phone company has two long distance plans as follows:
Plan 1: $4.95/month plus 5 cents/minutePlan 2: $2.75/month plus 7 cents/minute
How many minutes would you need to talk each month in order for Plan 1 to be more cost-effective than Plan 2?
64. Craig’s goal in math class is to obtain a “B” for the semester. His semester average is based on four equally weighted tests. So far, he has obtained scores of 84, 89, and 90. What range of scores could he receive on the fourth exam and still obtain a “B” for the semester? (Note: The minimum cutoff for a “B” is 80 percent, and an average of 90 or above will be considered an “A”.)
University of Houston Department of Mathematics96
SECTION 1.8 Absolute Value and Equations
Section 1.8: Absolute Value and Equations
Absolute Value
Absolute Value
Equations of the Form |x| = C:
Special Cases for |x| = C:
Example:
MATH 1300 Fundamentals of Mathematics 97
CHAPTER 1 Introductory Information and Review
Solution:
Example:
Solution:
University of Houston Department of Mathematics98
SECTION 1.8 Absolute Value and Equations
Example:
Solution:
Example:
Solution:
MATH 1300 Fundamentals of Mathematics 99
CHAPTER 1 Introductory Information and Review
Example:
Solution:
University of Houston Department of Mathematics100
SECTION 1.8 Absolute Value and Equations
Additional Example 1:
Solution:
Additional Example 2:
Solution:
MATH 1300 Fundamentals of Mathematics 101
CHAPTER 1 Introductory Information and Review
Additional Example 3:
Solution:
Additional Example 4:
Solution:
University of Houston Department of Mathematics102
SECTION 1.8 Absolute Value and Equations
Additional Example 5:
Solution:
MATH 1300 Fundamentals of Mathematics 103