Chapter 1

Chapter 1

Solving Equations and Inequalities

1.1 – Expressions and Formulas

1.1 – Expressions and Formulas

Order of Operations

1.1 – Expressions and Formulas

Order of Operations

Parentheses

1.1 – Expressions and Formulas

Order of Operations

Parentheses

Exponents

1.1 – Expressions and Formulas

Order of Operations

Parentheses

Exponents

Multiplication

1.1 – Expressions and Formulas

Order of Operations

Parentheses

Exponents

Multiplication

Division

1.1 – Expressions and Formulas

Order of Operations

Parentheses

Exponents

Multiplication

Division

Addition

1.1 – Expressions and Formulas

Order of Operations

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

1.1 – Expressions and Formulas

Order of Operations

Parentheses Please

Exponents

Multiplication

Division

Addition

Subtraction

1.1 – Expressions and Formulas

Order of Operations

Parentheses Please

Exponents Excuse

Multiplication

Division

Addition

Subtraction

1.1 – Expressions and Formulas

Order of Operations

Parentheses Please

Exponents Excuse

Multiplication My

Division

Addition

Subtraction

1.1 – Expressions and Formulas

Order of Operations

Parentheses Please

Exponents Excuse

Multiplication My

Division Dear

Addition

Subtraction

1.1 – Expressions and Formulas

Order of Operations

Parentheses Please

Exponents Excuse

Multiplication My

Division Dear

Addition Aunt

Subtraction

1.1 – Expressions and Formulas

Order of Operations

Parentheses Please

Exponents Excuse

Multiplication My

Division Dear

Addition Aunt

Subtraction Sally

Example 1

Example 1

Find the value of [2(10 - 4)2 + 3] ÷ 5.

Example 1

Find the value of [2(10 - 4)2 + 3] ÷ 5.

[2(10 - 4)2 + 3] ÷ 5 =

Example 1

Find the value of [2(10 - 4)2 + 3] ÷ 5.

[2(10 - 4)2 + 3] ÷ 5 = [2(6)2 + 3] ÷ 5

Example 1

Find the value of [2(10 - 4)2 + 3] ÷ 5.

[2(10 - 4)2 + 3] ÷ 5 = [2(6)2 + 3] ÷ 5

[2(36) + 3] ÷ 5

Example 1

Find the value of [2(10 - 4)2 + 3] ÷ 5.

[2(10 - 4)2 + 3] ÷ 5 = [2(6)2 + 3] ÷ 5

[2(36) + 3] ÷ 5

[72 + 3] ÷ 5

Example 1

Find the value of [2(10 - 4)2 + 3] ÷ 5.

[2(10 - 4)2 + 3] ÷ 5 = [2(6)2 + 3] ÷ 5

[2(36) + 3] ÷ 5

[72 + 3] ÷ 5

75 ÷ 5

Example 1

Find the value of [2(10 - 4)2 + 3] ÷ 5.

[2(10 - 4)2 + 3] ÷ 5 = [2(6)2 + 3] ÷ 5

[2(36) + 3] ÷ 5

[72 + 3] ÷ 5

75 ÷ 5

15

Example 2

Example 2

Evaluate x2 – y(x + y) if x = 8 and y = 1.5.

Example 2

Evaluate x2 – y(x + y) if x = 8 and y = 1.5.

x2 – y(x + y) =

Example 2

Evaluate x2 – y(x + y) if x = 8 and y = 1.5.

x2 – y(x + y) = 82 – 1.5(8 + 1.5)

Example 2

Evaluate x2 – y(x + y) if x = 8 and y = 1.5.

x2 – y(x + y) = 82 – 1.5(8 + 1.5)

82 – 1.5(8 + 1.5)

Example 2

Evaluate x2 – y(x + y) if x = 8 and y = 1.5.

x2 – y(x + y) = 82 – 1.5(8 + 1.5)

82 – 1.5(8 + 1.5)

82 – 1.5(9.5)

Example 2

Evaluate x2 – y(x + y) if x = 8 and y = 1.5.

x2 – y(x + y) = 82 – 1.5(8 + 1.5)

82 – 1.5(8 + 1.5)

82 – 1.5(9.5)

64 – 1.5(9.5)

Example 2

Evaluate x2 – y(x + y) if x = 8 and y = 1.5.

x2 – y(x + y) = 82 – 1.5(8 + 1.5)

82 – 1.5(8 + 1.5)

82 – 1.5(9.5)

64 – 1.5(9.5)

64 – 14.25

Example 2

Evaluate x2 – y(x + y) if x = 8 and y = 1.5.

x2 – y(x + y) = 82 – 1.5(8 + 1.5) 82 – 1.5(8 + 1.5)

82 – 1.5(9.5) 64 – 1.5(9.5) 64 – 14.25 49.75

Example 3

Example 3

Evaluate a3 + 2bc if a = 2, b = -4, and c = -3.

c2 – 5

Example 3

Evaluate a3 + 2bc if a = 2, b = -4, and c = -3.

c2 – 5

a3 + 2bc =

c2 – 5

Example 3

Evaluate a3 + 2bc if a = 2, b = -4, and c = -3.

c2 – 5

a3 + 2bc = 23 + 2(-4)(-3)

c2 – 5

Example 3

Evaluate a3 + 2bc if a = 2, b = -4, and c = -3.

c2 – 5

a3 + 2bc = 23 + 2(-4)(-3)

c2 – 5 (-3)2 – 5

Example 3

Evaluate a3 + 2bc if a = 2, b = -4, and c = -3.

c2 – 5

a3 + 2bc = 23 + 2(-4)(-3)

c2 – 5 (-3)2 – 5

= 8 + 2(-4)(-3)

Example 3

Evaluate a3 + 2bc if a = 2, b = -4, and c = -3.

c2 – 5

a3 + 2bc = 23 + 2(-4)(-3)

c2 – 5 (-3)2 – 5

= 8 + 2(-4)(-3)

9 – 5

Example 3

Evaluate a3 + 2bc if a = 2, b = -4, and c = -3.c2 – 5

a3 + 2bc = 23 + 2(-4)(-3) c2 – 5 (-3)2 – 5

= 8 + 2(-4)(-3) 9 – 5

= 8 + 24 9 – 5

Example 3

Evaluate a3 + 2bc if a = 2, b = -4, and c = -3.c2 – 5

a3 + 2bc = 23 + 2(-4)(-3) c2 – 5 (-3)2 – 5

= 8 + 2(-4)(-3) 9 – 5

= 8 + 24 9 – 5

= 32 4

Example 3

Evaluate a3 + 2bc if a = 2, b = -4, and c = -3.c2 – 5

a3 + 2bc = 23 + 2(-4)(-3) c2 – 5 (-3)2 – 5

= 8 + 2(-4)(-3) 9 – 5

= 8 + 24 9 – 5

= 32 = 8 4

Example 4

Example 4

Find the area of the following trapezoid. 16 in.

10 in.

52 in.

Example 4

Find the area of the following trapezoid. 16 in.

A = ½h(b1 + b2)

10 in.

52 in.

Example 4

Find the area of the following trapezoid. 16 in.

A = ½h(b1 + b2)

10 in.

52 in.

A = ½h(b1 + b2)

Example 4

Find the area of the following trapezoid. 16 in.

A = ½h(b1 + b2)

10 in. = h

52 in.

A = ½h(b1 + b2)

Example 4

Find the area of the following trapezoid. 16 in. = b1

A = ½h(b1 + b2)

10 in. = h

52 in.

A = ½h(b1 + b2)

Example 4

Find the area of the following trapezoid. 16 in. = b1

A = ½h(b1 + b2)

10 in. = h

52 in. = b2

A = ½h(b1 + b2)

Example 4

Find the area of the following trapezoid. 16 in.

A = ½h(b1 + b2)

10 in.

52 in.

A = ½h(b1 + b2)

= ½10(16 + 52)

Example 4

Find the area of the following trapezoid. 16 in.

A = ½h(b1 + b2)

10 in.

52 in.

A = ½h(b1 + b2)

= ½10(16 + 52)

= ½10(68)

Example 4

Find the area of the following trapezoid. 16 in.

A = ½h(b1 + b2)

10 in.

52 in.

A = ½h(b1 + b2)

= ½10(16 + 52)

= ½10(68)

= 5(68)

Example 4

Find the area of the following trapezoid. 16 in.

A = ½h(b1 + b2)

10 in.

52 in.

A = ½h(b1 + b2)

= ½10(16 + 52)

= ½10(68)

= 5(68) = 340

1.2 – Properties of Real Numbers

1.2 – Properties of Real Numbers

Real Numbers

1.2 – Properties of Real Numbers

Real Numbers (R)

1.2 – Properties of Real Numbers

Real Numbers (R)

1.2 – Properties of Real Numbers

Real Numbers (R)

Rational

1.2 – Properties of Real Numbers

Real Numbers (R)

Rational (⅓)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

Integers

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

Integers (-6)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

Whole #’s

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

Whole #’s (0)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

(W) Whole #’s (0)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

(W) Whole #’s (0)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

(W) Whole #’s (0)

Natural #’s

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

(W) Whole #’s (0)

Natural #’s (7)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

(W) Whole #’s (0)

(N) Natural #’s (7)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓)

(Z) Integers (-6)

(W) Whole #’s (0)

(N) Natural #’s (1)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓) Irrational

(Z) Integers (-6)

(W) Whole #’s (0)

(N) Natural #’s (1)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓) Irrational √ 5

(Z) Integers (-6)

(W) Whole #’s (0)

(N) Natural #’s (1)

1.2 – Properties of Real Numbers

Real Numbers (R)

(Q) Rational (⅓) (I) Irrational √ 5

(Z) Integers (-6)

(W) Whole #’s (0)

(N) Natural #’s (1)

Real

Rational Irrational Integers

Whole Natural

Example 1

Example 1

Name the sets of numbers to which each apply.

Example 1

Name the sets of numbers to which each apply.

Example 1

Name the sets of numbers to which each apply.

Example 1

Name the sets of numbers to which each apply.

(a) √ 16

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

(d) -⅞

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

(d) -⅞ - Q

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

(d) -⅞ - Q, R

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

(d) -⅞ - Q, R

__

(e) 0.45

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

(d) -⅞ - Q, R

__

(e) 0.45 - Q

Example 1

Name the sets of numbers to which each apply.

(a) √ 16 = 4 - N, W, Z, Q, R

(b) -185 - Z, Q, R

(c) √ 20 - I, R

(d) -⅞ - Q, R

__

(e) 0.45 - Q, R

Properties of Real Numbers

Property Addition Multiplication

Commutative a + b = b + a a·b = b·a

Associative (a+b)+c = a+(b+c) (a·b)·c = a·(b·c)

Identity a+0 = a = 0+a a·1 = a = 1·a

Inverse a+(-a) =0= -a+a a·1 =1= 1·a

a a

Distributive a(b+c)=ab+ac and (b+c)a=ba+ca

Example 2

Example 2

Name the property used in each equation.

Example 2

Name the property used in each equation.

(a) (5 + 7) + 8 = 8 + (5 + 7)

Example 2

Name the property used in each equation.

(a) (5 + 7) + 8 = 8 + (5 + 7)

Commutative Addition

Example 2

Name the property used in each equation.

(a) (5 + 7) + 8 = 8 + (5 + 7)

Commutative Addition

(b) 3(4x) = (3·4)x

Example 2

Name the property used in each equation.

(a) (5 + 7) + 8 = 8 + (5 + 7)

Commutative Addition

(b) 3(4x) = (3·4)x

Associative Multiplication

Example 3

What is the additive and multiplicative inverse for -1¾?

Example 3

What is the additive and multiplicative inverse for -1¾?

Additive: -1¾

Example 3

What is the additive and multiplicative inverse for -1¾?

Additive: -1¾ + = 0

Example 3

What is the additive and multiplicative inverse for -1¾?

Additive: -1¾ + 1¾ = 0

Example 3

What is the additive and multiplicative inverse for -1¾?

Additive: -1¾ + 1¾ = 0

Multiplicative: -1¾

Example 3

What is the additive and multiplicative inverse for -1¾?

Additive: -1¾ + 1¾ = 0

Multiplicative: -1¾ · = 1

Example 3

What is the additive and multiplicative inverse for -1¾?

Additive: -1¾ + 1¾ = 0

Multiplicative: (-1¾)(-4/7) = 1

Example 4

Example 4

Simplify 2(5m+n)+3(2m–4n).

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

10m

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

10m +

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

10m + 2n

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

10m + 2n +

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

10m + 2n + 6m

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

10m + 2n + 6m –

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

10m + 2n + 6m – 12n

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

10m + 2n + 6m – 12n

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

10m + 2n + 6m – 12n

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

10m + 2n + 6m – 12n

10m + 6m + 2n – 12n

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

10m + 2n + 6m – 12n

10m + 6m + 2n – 12n

16m

Example 4

Simplify 2(5m+n)+3(2m–4n).

2 (5m+n) + 3 (2m–4n)

2(5m)+2(n)+3(2m)-3(4n)

10m + 2n + 6m – 12n

10m + 6m + 2n – 12n

16m – 10n