8 123

123

8

4.1 : 1 4.2 : 1 2 6.1 : 1 2 6.2 : 1 6.3 : 1 6.4 : 1 2 6.5 : 1

1. 2. 3. 4. 5. 6.

8.1 (2 ) 8.2 (2 ) 8.3 (6 ) 8.4 (4 )

()

124 .1

. 15

88..11

: 1. 2. / : 1.

2. 3. 4. 5. 6. 7. : 1. 2. 3. 4. 5. 6.

MATH

Series

8 125

. 15

1 2 3 4 5 . . . n () 90 180 270 360 450 . . . 90n

1. 1, 2, 3, 4, 5, . . . 2. 90

2 180 902 n n 90 n 90n 90n n

3. n 90n 100 90100 9,000

4. 630 630 90 n 90n 630 630 7

1 3 1) 2, 4, 6, 8, 2) 13, 10, 7, 4, 3) 1, 4, 9, 16,

1) 2, 4, 6, 8, 2

2, 4, 6, 8, 10, 12, 14

2) 13, 10, 7, 4, 3 13, 10, 7, 4, 1, -2, -5

3) 1, 4, 9, 16, 1, 4, 9, 16, 25, 36, 49

126 .1

. 15

2 22 n 2, 4, 6, 8,

1 2 2 = 1 2 2 4 2 + 2 = 2 2 3 6 (2 + 2) + 2 = 3 2 4 8 (2 + 2 + 2) + 2 = 4 2 5 10 (2 + 2 + 2 + 2) + 2 = 5 2 10 22 2 = 44 n n 2 = 2n 10 2n

1. 3

1) 5, 8, 11, 14,

2) 15, 19, 23, 27,

3) 27, 32, 37, 42,

4) 100, 80, 60, 40,

5) 2, 4, 8, 16,

6) 1 2 3 4, , ,2 3 4 5 ,

8.1 :

8 127

. 15

2. 1)

1 2 3 4 5 ... 10 ... n 5 4 3 2 ... ...

2) 1 2 3 4 5 ... 10 ... n 1 3 5 7 ... ...

3) 1 2 3 4 5 ... 10 ... n -5 -10 -15 -20 ... ...

4) 1 2 3 4 5 ... 10 ... n 0.1 0.2 0.3 0.4 ... ...

5) 1 2 3 4 5 ... 10 ... n 1 4 9 16 ... ...

3. 150

1 2 3 4 5 ... n 5 6 7 8 9 ?

1 ( 5) 1 4 1 + 4 = 5 2 ( 6) 2 + 4 = 3 ( 7) 3 + .. = 4 ( 8) + = 8 5 ( 9) + = n + .. 150 ..+ = .

128 .1

. 15

4. 249

1 2 3 1 1 ( ........) .......... ......... 1

2 (....... ........) ........ .......... 3 (....... ........) ........ .......... 4 (....... ........) ........ .......... 5 (....... ........) ........ .......... n (....... ........) ........ ..........

249

1 2 3 4 5 n 3 5

1 2 3

2 3 2 3

8 129

. 15

88..22

: 1. 2. 3. / : 1.

2. 3. 4. 5. 6. 7. : 1. 2. 3. 4. 5. 6.

MATH

Series

130 .1

. 15

55 45 2 2x + y 1>

x + 2 = 27 a + b = b + a

x + 3 < 9 5 533 =2 2

=

5 + 7 = 12 18 2 = 10 8 + 9 = 19 29 5 = 24

=

x 6 = 5 x + 4 = -7 x + 9 = -2 x 9 = 2

=

8 131

. 15

1. y + 2 = -3 -5 -5 + 2 = -3 / 2. y + 2 = -3 3 -5 + 3 -3 / 3. x + 5 = 8 3 4. x + 5 = 8 2

1 x 2 = 5 2 = 5 x 7 x 2 = 5

x 2 = 5

2 n2 = 16

= 16 n 4 n2 = 16

(-4)2 = 16 n -4 n2 = 16

n2 = 16 -4

132 .1

. 15

3 b + 3 = 3 + b b b + 3 = 3 + b

b + 3 = 3 + b

4 y + 7 = y y y + 7 = y

y + 7 = y

3

1. 1 2 2. 3 3. 4

8 133

. 15

1. /

1 4 + x = 8 4 2 z 3 = 7 11

3 a6 1 = -12 6

4 x + 7 = 7 x -7

5 6x 1 = 9 106

6 18 3x = 9 3

7 c = 6-30 180

8 -7.6 = x 1.4 6.2 9 1.2 + b = 4.8 3.6

10 -m 5 = -9.5 -7.5

11 x - 38 = 1 11

12 3 1= m -2 2 2

13 2a + 3a = 5 -1

14 2x + 53 = 1 -1

15 y + 2 = y 0

8.2 :

134 .1

. 15

2.

1 x 6 = 17 2 2b = 15 3 s 17 = 0

4 -t = 0 5 x 5 = x + 5 6 2x + 3 = 3 + 2x 7 x3 = -1

8 y2 = 9

9 -3x = 3x 10 3x 2 = 4 11 m + 3 = m 12 5x2 = 20

13 r2 = 100 1

14 z3 = -1000

15 3n n = 2n

3. x 11 -5 x 11 = -5 x = 6 1) 2x 12 6

2) x 6 15

3) x 3 16

4) y -9

5) y 3 y 20

8 135

. 15

: 1. 2. 3. / : 1.

2. 3. 4. 5. 6. 7. : 1. 2. 3. 4. 5. 6.

88..33

MATH

Series

136 .1

. 15

1) x = 5 5 = x 2) a + b = c c = a + b 3) -3 = -6z 4) x = y

1) x = y y = 5 x = 5 2) a + b = x x = -8 a + b = -8 3) A = mN mN = B 4) x = y y = z

1) 1 + 2 = 3 2) (1 + 2) + 5 = 3 + 5 3) (1 + 2) + (-7) = 3 + (-7)

a = b b = a a b

a = b b = c a = c a, b c

8 137

. 15

4) 8 = 24 5) 8 + 6 = (24) + 6 6) 8 + (-1) = (24) + (-1)

a = b a + (-c) = b + (-c) a c = b c a, b c

1) 1 + 2 = 3 2) (1 + 2)5 = 35 3) (1 + 2) (-7) = 3(-7) 4) 8 = 24 5) 86 = (24)6 6) 8 (-1) = (24)(-1)

a = b a + c = b + c a, b c

a = b a c = b c a, b c

a = b ac = bc a, b c

138 .1

. 15

x = y 0.1x = 0.1y x y

a = b, c 0 1 1a = bc c a b=c c a, b c

1.

1) x = 18 x + 5 = 18 +

2) y = 27 = 27 + 9

3) z = 60 z 25 =

4) 85 = p + 13 = p + 13

5) (m 2) = 48 (m 2) + 15 =

8.3 :

a = b a b=c c a, b c c 0

1. a = b b = a a b

2. a = b b = c a = c a, b c

3. a = b a + c = b + c a, b c a = b a c = b c a, b c

4. a = b ac = bc a, b c

a = b a b=c c a, b c c 0

8 139

. 15

6) a = 15 a 8 = 15

7) b = 23 . = 23 9

8) c = 31 c 17 =

9) (e 5) = 48 = 48 11

10) 52 = (f + 10) 52 9 =

2.

1) a = 9 a8 =

2) b = c = 12c

3) c = a c15 =

4) x = 1315 x 1515 =

5) z = 2112 z 1212 =

6) a = 12 a4 =

7) b = x = 18x

8) c = 36 c9 =

9) y = 48 y6 =

10) x = z xy = 0y

x + 5 = 8

140 .1

. 15

(1) (x + 5) + (-5) = 8 + (-5) -5 x + 5 8

(2) x + [5 + (-5)] = 8 + (-5)

(3) x + 0 = 3 x + [5 + (-5)] = x + 0 x + 0 = x + [5 + (-5)] 8 + (-5) = 3 x + 0 = x + [5 + (-5)] x + [5 + (-5)] = 8 + (-5) 8 + (-5) = 3 x + 0 = 3

(4) x = 3 (5) x = 3 x + 5 = 8

3 + 5 = 8 x + 5 = 8 3

1 x 15 = 21 x 15 = 21

15 x 15 + 15 = 21 + 15 x = 36

x = 36 x 15 = 21 36 15 = 21

21 = 21 36 x 15 = 21 36

2 x + 28 = 46 x + 28 = 46

28

8 141

. 15

x + 28 28 = 46 28 =

x = x + 28 = 46 + 28 = 46

= 56 x + 28 = 46

3 4x = -12 4x = -12

4

4x4 = -124

=

x = 4x = -12 4 = -12

= -12 4x = 12

4 x9

= 6

x9

= 6

9

x99 = 69

=

x = x9

= 6

= 6

= 6

2,000

142 .1

. 15

x9

= 6

1) m 3 = 7

2) b + 5 = 16

2) s 15 = -17

4) 12 + g = -14

8.4 :

8 143

143

5) t 2.6 = 1.2

6) 1.3 = -4.8 + a

7) 5y = 45

8) 6x = -42

9) -0.3w = 2.4

10) -0.7w = -4.9

144 .1

. 15

11) 1 y 86

12) 5 x 108

13) z 2.50.2

14) a 143

5 x + 2 = -73

x + 2 = -73

2

x3 + 2 2 = -7 2

=

3 =

=

8 145

. 15

x = x + 2 = -73

-27 + 2 = - 73

-9 + 2 = 7 -7 = -7

x + 2 = -73

6 8x 4 = 12 8x 4 = 12

4 8x 4 + 4 = 12 + 4

= 8 = =

x = 8x 4 = 12 8(2) 4 = 12

16 4 = 12 12 = 12

8x 4 = 12

7 35x + = 12

35x + = 12

32

3 3 35x + - = 1-2 2 2

=

1,850

146 .1

. 15

1-5x 2= 5 5

1 1x = - 2 5

=

x = 35x + = 12

1 35 - + = 110 2

1 3- + = 12 2

2 = 12

35x + = 12

8 1 (c + 3) = 12

1 (c + 3) = 12

12 (c + 3) = 212

c + 3 = 2 = =

c = 1 (c + 3) = 12

1 (.......... + 3) = 12

1 (2) = 12

1 = 1

1 (c + 3) = 12

.. 250

8 147

. 15

9 3(x + 7) = 154

3(x + 7) = 154

43

3(x + 7) 4 4 = 154 3 3 x + 7 = 20

=

x =

x = 3(x + 7) = 154

3(........ + 7) = 154

3(20) = 154 15 = 15

3(x + 7) = 154

10 5x 3 = 3x + 5 5x 3 = 3x + 5

3 5x 3 + 3 = 3x + 5 + 3

= 3x =

=

=

=

148 .1

. 15

x = 5x 3 = 3x + 5 5() 3 = 3() + 5

= =

5x 3 = 3x + 5

11 6 + 2x 5x + 3=4 6

... 4 6 12 12

6 + 2x 5x + 312( ) = 12( )4 6

3(6 + 2x) = 2(5x + 3) =

10x 18 + 6x -10x = 10x + 6-10x

18- 4x = 6 18 18- 4x -18 = 6-18

-4x = -12

=

=

x = 6 + 2x 5x + 3=4 6

6 + 2(......) 5(......) + 3=4 6

=

6 + 2x 5x + 3=4 6

.. 4 = 6 = .. 4 6

.

8 149

. 15

1) b - 9 = 532

2) 4x + 7 = 27

3) 6(x - 2) = 42

4) 9c -8 = 46

8.5 :

150 .1

. 15

5) a - 23 = 127

6) 2 + x = 84

7) s + 75 = 829

8) 17 + y = 232

8 151

. 15

9) 4x 2x = -13 5-

10) 12x + 3(x 2) = 0

11) 2 10(3 + 2a) =7 7

12) 2x 1 x 4+ = +3 5 3 5

152 .1

152

: 1. 2. 3. 4. / : 1.

2. 3. 4. 5. 6. 7. : 1. 2. 3. 4. 5. 6.

88..44

MATH

Series

8 153

. 15

a, b, c, x, y x

10

25 x

1 3 15 x x + 3 = 15

2 13 6 .. .

3 60 .. .

4 12 .. .

5 5 20 .. .

6 2 400 .. .

154 .1

. 15

7 5 70 .. .

8 2 500 .. .. .

x

1. 15 5.5

2. 3 15

3. 4 36

4. 6 40

5. 1,290 350

6. ..1847 ..1879

8.6 :

8 155

. 15

9 10 28 x

.... 10 .. 10 28 ... ... ... ... ...

x .. ..

5

1 2 3 4 5

156 .1

. 15

10 10 x

x

11 3 2 19

x

3

3 3 2

x =

3 + 3 = 3 + 3 = 3 2

8 157

. 15

12 15

50 250

15

1 x5

50 250

50

5

158 .1

. 15

1. 15 60

2. 3 8

8.7 :

8 159

. 15

3. 1,000

250

160 .1

. 15

4. 30

5. 6 64

3

8 161

. 15

...

27 x

7 3x 11

x + 5

x 2

3 3x 9

162 .1

. 15

...

100 5 5

P