15.1 – 15.3 key
1a) T
b) F, 5 – 8 = -3
c) T
d) F, 1/4 = 0.25
e) F, 3/0 is undefined
2a) 𝑥 = 2
natural, whole, integer, rational
b) 𝑥 = ±√5
irrational
1
c) 𝑥 = 3
rational
d) 𝑥 = 0
whole, integer, rational
3) Student 1 is correct
4a) 10, 31, 1970
3
−4
b) 8, −15, 8 , 0, 9.5, 5 , 857
c) √2, 𝜋
4
5a) 9
b)
c)
6a)
b)
c)
d)
e)
f)
7)
8a)
b)
c)
9a)
b)
c)
d)
e)
f)
10a)
81
9
= 11
99
581
999
Associative Property of Multiplication
Distributive Property of Multiplication
Commutative Property of Addition
Multiplicative Inverse
Multiplicative Identity
Additive Inverse
see next page
1
−1
−𝑖
9 − 8𝑖
5 + 𝑖√3
8 + 2𝑖√3
4𝑥𝑖 + 7𝑖
𝑥 2 − 2𝑥𝑖 − 1
8𝑥 2 − 6𝑥𝑖 + 2
𝑥 = 0, 4
5±𝑖√15
b)
4
c) inequality form
1
𝑥 < −2
𝑥>3
interval notation
−1
(−∞, 2 ) , (3, ∞)
11) 1800°
12) 72°
7a
3(3x - 8) + 2
9x – 24 + 2
9x – 22
9x – 22 + 22
9x + 0
9x
9x
1
9x ∙ 9
=
=
=
=
=
=
=
=
1
32
32
32
32 + 22
32 + 22
32 + 22
54
1
54 ∙ 9
Distributive Property
Combine like terms
Addition Property of Equality (add same thing to both sides)
Combine like terms (left side)
Additive Identity (a + 0 = a, left side)
Combine like terms
Multiplication Property of Equality (multiply both sides by same thing)
1
Commutative Property of Multiplication (a ∙ b = b ∙ a, left side)
1
Multiply (left side)
1
Multiplicative Identity (a ∙ 1 = a, left side)
Multiply
x(9) ∙ 9 = 54 ∙ 9
x(1) = 54 ∙ 9
x = 54 ∙ 9
x = 6
7b
5(3 + 6x) – 25
15 + 30x – 25
30x + 15 – 25
30x – 10
30x – 10 + 10
30x + 0
30x
30x
1
30x ∙ 30
1
=
=
=
=
=
=
=
=
=
20
20
20
20
20 + 10
20 + 10
20 + 10
30
1
30 ∙ 30
1
x(30) ∙ 30 = 30 ∙ 30
x(1) = 1
x = 1
Distributive Property
Commutative Property of Addition
Combine like terms
Addition Property of Equality
Combine like terms
Additive Identity
Combine like terms
Multiplication Property of Equality
Commutative Property of Multiplication
Multiply
Multiplicative Identity