AlgExtraPractice-solutions

[ Pobierz całość w formacie PDF ]
Practice 1
Practice 2
Practice 3
1) (-3) + (-6) = -9
1) 24 = 2 x 2 x 2 x 3
48 = 2 x 2 x 2 x 2 x 2 x 3
LCM = 2 x 2 x 2 x 2 x 3 = 48
13)

4 · 6
2

=

4 · 36

= 144
1) -4A + 3 + 7A - 2 = 8 + 2
3A + 1 = 10
3A = 10 -1
3A = 9
A = 3
8) 10R + 2R - 9 = 10 - 7
12R - 9 = 3
12R = 12
R = 1
2) (2) + (-5) = -3
3) (-7) + (-1) = -8
2) 10 = 2 x 5
15 = 3 x 5
LCM = 2 x 3 x 5 = 30
14)

5 - 2
3

=

5 - 8

=

-3

=3
4) (-3) - (-6) = (-3) + 6 = + 3
Check: -4(3) + 3 + 7(3) - 2 = 8 + 2
-12 + 3 + 21 - 2 = 8 + 2
10 = 10
9) C = C - 4 + 8C = 2C + 2 • 6
10C - 4 = 2C + 12
8C = 16
C = 2
5) (+2) - (+5) = -3
15)

-3
2
· 7
2

=

-9 - 49

=

-58

= 58
3) 9 = 3 x 3
11 =1 x 11
LCM = 3 x 3 x 11 = 99
6) (-7) - (-4) = (-7) + 4 = -3
7) (5)(-4) = -20
2) 2C - C + 8 + 3C = 16
4C = 8 = 16
4C = 8
C = 2
16)

9
2
- 3
2

=

81 - 9

=

72

= 72
10) 12 ÷ 4 + 6X = 25 + 26
3 + 6X = 51
6X = 48
X = 8
8) (-3)(-6) = +18
4) 35 = 5 x 7
56 = 2 x 2 x 2 x 7
LCM = 2 x 2 x 2 x 5 x 7 = 280
9) (-1)(2) = -2
17) -5
2
+

1
2
- 5
2

+ (2 x 3
2
) =
-25 +

1 - 25

+ (2 x 9) =
-25 +

-24

+ 18 =
-25 + 24 + 18 = 17
18) 6 + 3 ÷ 3 - 8 + 4 x 5 =
6 + (3 ÷ 3) - 8 + (4 x 5) =
6 + 1 - 8 + 20 =
7 - 8 + 20 =
-1 + 20 = 19
Check: to check each equation,
substitute the solution for the
unknown and simplify.
10) negative
5) 36 = 2 x 2 x 3 x 3
25 = 5 x 5
LCM = 2 x 2 x 3 x 3 x 5 x 5 = 900
11) -2Y - 2 - 5Y + 9Y + 4 = 3 • 4
2Y + 4 = 12
2Y = 8
Y = 4
11) positive
12) negative
3) -5Y + 7 + 8Y + 4 + Y = 15
4Y + 11= 15
4Y = 4
Y = 1
13) (-16) ÷ (-4) = +4
6) 54 = 2 x 3 x 3 x 3
32 = 2 x 2 x 2 x 2 x 2
LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 = 864
14) (-20) ÷ (5) = -4
12) -8 + 2E + 5 - E + 5E = 3
2
+ 6
6E - 3 = 9 + 6
6E - 3 = 15
6E = 12
E = 2
15) (32) ÷ (-8) = -4
7) -3
2
• 2 + 2
2
=
-9 • 2 + 4 =
-18 + 4 = -14
4) B + 2B - 8 + 5B = (3 • 4) + 4
8B - 8 = 16
8B = 24
B = 3
16) (-8)
2
= 64
17) -8
2
= -64
18) -(8)
2
= -64
8) 10 • 3
2
+ 18
10 + 9 + 18 = 108
5) 4K + 2 + 2K + K - 2 = 7
2
7K + 2 - 2 = 49
7K = 49
K = 7
13) 2R - 8R + 3 + 7R = 10
R + 3 = 10
R = 7
19) 6X - 7Y - 4Y + 11X - 8 =
17X - 11Y - 8
9) (-5)
2
• 9 ÷ 3 =
25 • 9 ÷ 3
225 ÷ 3 =75
20) 9X + 2Y + 3X - Y =
12X + Y
6) 7Q - 4Q + 10 - 9 + Q = 22 - 1
4Q + 1 = 21
4Q = 20
Q = 5
14) 8 - 6 + 7Z + 5Z = (100 • 2) ÷ 4
12Z + 2 = 200 ÷ 4
12Z + 2 = 50
12Z = 48
Z = 4
21) 12B + 8A - 9A - 10B =
2B - A
10) 14(2 + 1
2
) - 4 =
14(3) - 4
42 - 4 = 38
22) 4C - 3D + 7C - 4 + 3 =
11C - 3D - 1
11) 9 + 33 ÷ 3 - 7
2
=
9 + 11 - 49 = 20 -49 = 29
7) 6 + 5A = 3A + 18
5A - 3A = + 18 - 6
2A = 12
A = 6
23) false
24) true
12) 4X - 4Y + 6X + 5Y - 1 =
10X + Y - 1
25) true
Practice 4
Practice 5
1) 6(3 + 2) = 6(3) + 6(2) = 18 + 12 = 30
1) (-2, 4)
2) 7(3 + 4 + 1) = 7(3) + 7(4) + 7 (1) = 121 + 28 + 7 = 56
2) II
3) 5(X + Y) = 5X + 5Y
4) 2(4M + 2Q) = 8M + 4Q
3) (6, 3)
5) 3(A + 3B - 2 + 4A) = 3A + 9B - 6 + 12A =
15A + 9B - 6
4) I
6) 4(X + 2Y + 4 + X) = 4X + 8Y + 16 + 4X =
8X + 8Y + 16
5) (2, 1)
6) I
7) done
8) 4A - 8B = 4(A - 2B)
7) (4, -4)
9) 21X + 14Y = 7(3X + 2Y)
8) IV
10) -5M -10N = -5(M + 2N)
9) (-4, -3)
11) 5B + 15C = 5 (B + 3C)
12) -5X + 20A = -5(X - 4A)
10) III
13) done
11) on the graph
14) 8B + 16 = 56
8(B + 2) = 8(7)
B + 2 = 7
B = 5
12) II
Y
13) on the graph
15) 12X - 36 + 36X = 60
48X - 36 = 60
12(4X - 3) = 12(5)
4X - 3 = 5
4X = 8
X = 2
In #15 and #16, terms were combined to
simplify before finding the common factor.
You could also find the common factor first
and then simplify. Either method should
yield the same answer.
14) I
•
F
•
H
15) on the graph
X
16) IV
16) 6Y - 12 - 3Y = 18
3Y - 12 = 18
3(Y - 4) = 3(6)
Y - 4 = 6
Y = 10
17) (0, 0)
•
J
18) negative, positive
19) X value
17) 5A + 20 = 30
5(A + 4) = 5(6)
A + 4 = 6
A = 2
20) 4
18) 2Q - 14 = 24
2(Q - 7) = 2(12)
Q - 7 = 12
Q = 19
Practice 6
Practice 7A and 7B
Practice 9
Use after lesson 8 if you have 35 lessons.
1) hours pies
0
1
2
pies
1) done
1) on the graph
-2
1
4
•
2) done
2) slope =
−
2
1
= -2
3) y-intercept = -1
•
3) slope-intercept
4) Y = -2X - 1
5) A and B
6) on the graph
7) Y = -2X + 5
8) 2X + Y = 5
hours
2) on the graph
•
4) 0
3) P = 3H - 2
5) 4
6) 2
4) hours arr.
0
1
2
arrangements
#3
#6
Y
•
3
4
5
•
7) answers will vary:
ex: Y = 3X
•
•
•
8) C
•
•
hours
X
5) on the graph
9) E
6) A = H + 3
10) D
7) hours problems
0
1
2
11) B
2
6
10
problems
•
9) on the graph
12) A
10) slope =
1
2
•
13) on the graph
11) y-intercept = 0
hours
14) on the graph
2
X
13) B and C
14) on the graph
Y
=
1
8) on the graph
15) on the graph
9) P = 4H + 2
1
2
X + 2
16) on the graph
15) Y =
10) X
Y
16) X - 2Y = -4
Y
#13
Y
0
1
2
1
4
7
#15
Y
#16
•
•
•
X
X
X
11) on the graph
#14
#14
•
•
12) Answers will vary. Your
problem should start with a
positive amount.
#9
12)
Practice 10
Practice 11
Practice 12
1) on the graph
1) on the graph
1) Y = -2X + 4 see graph
Y
2) slope =
−
1
1
= −
1
2) 0 = -4/5(2) + b
y-intercept = 1 3/5
•
3) Y = -4/5 X + 1 3/5
2) dotted
3) y-intercept = 4
4) 4X + 5Y = 8
•
4) Y = -X + 4
5) B and C
6) on the graph
Y
#5
•
X
3) (0, 0) 2(0) + (0) < 4, 0 < 4 true
(2, 2) 2(2) + (2) < 4, 6 < 4 false
•
•
7) Y = X - 1
8) X - Y = 1
4) see graph
•
X
#3
Y
Y
5) see graph
#6
•
#1
•
6) solid
•
4
−
(
−
3)
0
−
(
−
2)
7
2
(see graph)
X
5)
=
•
•
X
•
7) (0, 0) (0) ≤ -3(0) - 1; 0 ≤ -1 false
(-1, 0) (0) ≤ -3(-1) - 1; 0 ≤ 2 true
6) 4 = 7/2(0) + b
4 = 0 + b; 4 = b
7) Y = 7/2 X + 4
8) -7/2 X + Y = 4; -7X + 2Y = 8; 7X - 2Y = -8
•
8) see graph
9) (3) = 1(0) + b
3 = b
Y = X + 3
Y
9) on the graph
9) X - 2Y = 2; Y = 1/2 X - 1; see graph
10) slope =
1
2
10) (1) = -1/2(-1) + b
1 = 1/2 + b; b = 1/2
Y = -1/2X + 1/2
10) solid
11) Y-intercept = 0
11) (2) = -2/3(-1) + b
2 = 2/3 + b; b = 1 1/3
Y = -2/3X + 1 1/3
12) (3) = 3/4(2) + b
3 = 3/2 + b; b = 1 1/2
Y = 3/4X + 1 1/2
13) (-3) = 2(-2) + b
-3 = -4 + b; 1 = b
Y = 2X + 1
14) (0) = 4(2) + b
0 = 8 + b; -8 = b
Y = 4X - 8
•
•
•
X
1
2
X
•
12)
Y
=
11) (0, 0) (0) - 2(0) ≤ 2; 0 ≤ 2 true
(3, 0) (3) - 2(0) ≤ 2, 3 ≤ 2 false
13) C
14) on the graph
15) Y = -2X + 3
12) see graph
16) 2X + Y = 3
Y
13) -4Y > -X + 2
Y < 1/4 X - 1/2
15)
2
−
3
−
1
−
2
=
−
1
−
3
=
1
3
=
m
14) 3Y ≤ 2X = 5
Y ≤ 2/3 X + 1 2/3
#11
(3) = 1/3(2) + b
3 = 2/3 + b; 2 1/3 = b
Y = 1/3 X + 2 1/3
X
2
−
(
−
2)
=
3
15) -5Y < -5X - 15
Y > X + 3
•
•
16)
4
=
m
(0) = 3/4(2) + b
3 = 3/2 + b; -1 1/2 = b
Y = 3/4 X - 1 1/2
•
#14
0
−
(
−
3)
Practice 13
Practice 14
1) on the graph
#5 d
Y
#1 a
#4 c
Y
2) on the graph
1) (2, 1)
#2 b
3) (-3, -1)
·
X
2) X + 2(3X - 5) = 4
X + 6X - 10 = 4
7X = 14, X = 2
X
4) on the graph
·
·
5) on the graph
6) (1, -3)
3) (2) + 2Y = 4
2Y = 2, Y = 1
4) (6, 3)
Y
Y
7) on the graph
5) X - 3(1/2 X) = -3
X - 1 1/2 X = -3
-1/2 X = -3, X = 6
·
8) on the graph
·
9) (-2, 0)
X
·
X
10) on the graph
6) Y = 1/2(6)
Y = 3
11) on the graph
#11 h
#8 f
12) (0, 3)
7) (-1, 3)
#7 e
#10 g
8) -2(-Y+ 2) + Y = 5
2Y - 4 + Y = 5
2Y + Y = 5 + 4
3Y = 9, Y = 3
Y
13) on the graph
Y
#16 r
·
14) on the graph
·
9) X + 3 = 2
X = -1
X
15) (-2, 0)
·
X
16) on the graph
10) 5X - 3(-2/3 X + 3) = 12
5X + 2X - 9 = 12
7X = 21, X = 3
2(3) + 3Y = 9
6 + 3Y = 9
3Y = 3, Y = 1
(3, 1)
17) on the graph
18) (3, 4)
#13 j
#17 s
#14 k
[ Pobierz całość w formacie PDF ]