1. 1
10
(4)

2. 1
1
1.
2.
3. –
4.

3. 5.
6.
2
4
4.2
(mathematical model)

4. 4.2 1
3

5. . . .
-
-
-

6. 4

7. 5
10
3
---------------------------------------------------------------
1) 2x+3 = x-5

8. -8 2
8 5
2 2
2) 9x+9 = 3x-4
,
3) 3x+9 = 2x
9 9
2
9
-9
2
6
4) x+9 = 2x

9. 5) 8x+ 5 = x
-12 5
7
5
-2
7
6) 8x + 9 = - x
1 9
2
9
-1
2
7) 3(a – 5) = 9
9 8
2 24
8) ( a + 5 ) = 23
82 9
2
9
41
2
9) 5x - 48 = 73 - 6x
9 9
2
11 121
10) - =
82 15
9
41
2

10. 7
5x+3 = 3x-5
5x+3 = 3x-5
-3x)
5x+3+ -3x) = 3x - 5 + -3x)
2x+3 = -5
-3)
2x+3+ -3) =
- 5 + -3)
2x = -8
1
2
2x 1
= -8 1
2 2
x = -4
x -4
5x+3 = 3x-5

11. 5(-4) +3 = 3(-4) -
5
(-20) +3 = (-12)
-5
-17 = -17
-4
5x+3 = 3x-5
8
1
1) 4x -3 = 2x
4x -3 = 2x
-2x
4x -3 + …………….= 2x +………….

12. 2x-3 =
2x-3 + =
2x =
1
2
2x 1
= ………. 1
2 2
x = ……………
x
………….. 4x -3 = 2x
4(…….) -3 = 2(……)
=
…………….
…………………. ………….
4x -3 = 2x
9

13. 2) 7x +5 = 2x
7x +5 = 2x
……….
7x +5 + …………….= 2x
+………….
5x +5 =
(-5)
5x +5 +
=
5x =
1
5
5x 1
= ………. 1
5 5
x = ……………
x
………….. 7x +5 = 2x

14. 7(…….) +5 =
2(……)
=
…………….
…………………. ………….
7x +5 = 2x
10
3) 5x = 9+4x
5x = 9+4x
……….
5x + …………….= 9+4x
+………….

15. x =
………………..
x
………….. 5x = 9+4x
5(…….) =
9+4(……..)
=
…………….
…………………. = ………….
5x = 9+4x

16. 11
4) 3x -2 = 2x + 3

17. 12

18. 2
1
a+ 3 ) = 1
2
1
a+ 3 ) = 1
2
2
1
a+ 3 ) 2 = 1 2
2
a+3 = 2
-3)
a + 3 + -3) =
2 + -3)
x = -1
x -1 1
2
a+ 3 ) = 1
1
(-1) + 3 ) = 1
2
2
= 1
2

19. 1= 1
-1
1
a+ 3 ) = 1
2
13
2
1)
3
a+ 5 ) = 24
5
3
a+ 5 ) = 24
5
5
3
a+ 5 ) 5 = 24 5
5
3(a + 5) = …………..
3(a + 5) ……………. =
120 ………….

20. a+5 =
(-5)
a + 3 +(-5)
=
a =
a
3
a+ 5 ) = 24
5
3
+5) =
5
24
3
…….
5
= 24
………. =
24
……… = 24
……….
3
a+ 5 ) = 24
5

21. 14
2) 2 x - 10 ) = 40
2 x - 10 ) = 40
1
2
2 x - 10 ) 1
= 40 1
2 2
……………….= 20
……………..
…………. = 20 +10
x = 30
x 30
2 x - 10 ) = 40
……………
= 40
2(20) = 40
40 = 40

22. 30
2 x - 10 ) = 40
15
3)
2
3+ 2a ) = 10
7 7
2
3+ 2a ) = 10
7 7
7
2
3+ 2a ) ………. = 10
7 7
……….
2 3+ 2a )
= ………………..

23. 2 3+ 2a ) ………….
= 10 ……………
3+ 2a =5
3+ 2a +………. = 5
+………….
2a = 2
1
2
2a 1
= 2 1
2 2
a = …………
a ………
2
3+ 2a ) = 10
7 7
2
3+ 2(……..) )
7
= 10
7
2
………. = 10
7 7
10
=
7
10
7

24. 2
3+ 2a ) = 10
7 7
16
4) 4 3+ 5a ) = 4 a

26. 17
3
1) =
=
………..
…….. = ……
……….. = ………..
-x
2x +(-x) = x -
2+(-x)
x = ……..

27. x …….
=
= …………
-1 = -1
-1 =
18
2) - = 2
- = 2
- = 2
= 2

28. 12
12 = 2 12
x = …….
x ……
- = 2
- = 2
8- 6 = 2
……. -
= 2
19

29. 3) + = 20
+ = 20
+ = 20
= 20
= 20
x =
x
+ = 20
+ = 20
8 + 12 = 20
+
= 20

30. 4) = + 24

32. 20
---------------------------------------------------------------
1) 9x+9 = 3x-4
,

33. 2) 3x+9 = 2x
9 9
2
9
-9
2
3) 8x+ 5 = x
-12 5
7
5
-2
7
21
4) 2x+3 = x-5
8
2
2
-8 5
2
5) x+9 = 2x
6) 8x + 9 = - x
-1 9
2

34. 9
1
2
7) 3(a – 5) = 9
9 24
2 8
8) ( a + 5 ) = 23
41 9
2
9
82
2
9) 5x - 48 = 73 - 6x
9 11
9
121
2
10) - =
15 82
9
41
2
22

35. 23
1
1) 4x -3 = 2x

36. 4x -3 = 2x
-2x
4x -3 +(-2x ) = 2x + 2x +(-2x
)
2x-3 = 0
3
2x-3 + 3 =
0+3
2x = 3
1
2
2x 1
= 3 1
2 2
x = 3
2
x 3
4x
2
-3 = 2x
4( 3 ) -3 = 2( 3
)
2 2
6-3 = 6
2
3=3
.
3
4x -3 = 2x
2

37. 24
2) 7x +5 = 2x
7x +5 = 2x
(-2x)
7x +5 + (-2x) = 2x + (-2x)
5x +5 = 0
(-5)
5x +5 + (-5) =
0+ (-5)
5x = -5
1
5
5x 1
= -5 1
5 5
x = -1
x -1
7x +5 = 2x

38. 7(-1) +5 = 2(-1)
-7+5 =
2
-2 = -2
-
-1 7x +5 = 2x
25
3) 5x= 9+4x
5x = 9+4x
(-4x)
5x + (-4x) = 9+4x + (-4x)
x = 9

39. x 9 5x
= 9+4x
5( 9 ) = 9+4( 9 )
45 = 9+36
45 = 45
9 5x = 9+4x
26

40. 4) 3x -2 = 2x + 3
3x -2 = 2x + 3
(-2x)
3x -2 + (-2x) = 2x +3+ (-2x)
x -2 = 3
2
x -2+2 =
3+2
x = 5
x 5
3x -2 = 2x + 3
3(5) -2 = 2(5) +
3
15-2 = 10+3
13 = 13

41. 5 3x -2 = 2x
+3
27
2
1) 3
a+ 5 ) = 24
5
3
a+ 5 ) = 24
5
5
3
a+ 5 ) 5 = 24 5
5
3
a+ 5 ) = 24 5
5
3(a + 5) = 120
1
3

42. 3(a + 5) 1
=
3
120 1
3
a+5 = 35
(-5)
a + 3 +(-5) = 40 +(-5)
a = 35
a 35
3
a+ 5 ) = 24
5
3
35 + 5 ) =
5
24
3
40 =
5
24
120
= 24
5
24 = 24
35
3
a+ 5 ) = 24
5
29

43. 2) 2 x - 10 ) = 40
2 x - 10 ) = 40
1
2
2 x - 10 ) 1
= 40 1
2 2
x - 10 = 20
10
x – 10+10 = 20 +10
x = 30
x 30
2 x - 10 ) = 40
2 30 - 10 )
= 40
2(20) = 40
40 = 40
30
2 x - 10 ) = 40

44. 30
3) 2
3+ 2a ) = 10
7 7
2
3+ 2a ) = 10
7 7
7
2
3+ 2a ) 7 = 10
7
7 7
2 3+ 2a ) = 10
1
2
2 3+ 2a ) 1
=
2
10 1
2
3+ 2a =5
(-3)

45. 3+ 2a +(-3) = 5 +(-3)
2a = 2
1
2
2a 1
= 2 1
2 2
a = 1
a 1 2
7
3+ 2a ) = 10
7
2
3+ 2(1) ) =
7
10
7
2
5= 10
7 7
10
= 10
7 7
1
2
3+ 2a ) = 10
7 7
31
4) 4 4+ 5a ) = 4 a

46. 4 4+ 5a ) = 4 a
1
4
4 4 + 5a ) 1
= 4a 1
4 4
4+ 5a = a
(-a )
4 + 5a + (-a ) = a + (-a )
4 + 4a = 0
(-4)
4+ 4a +(-4) = 0 +(-4)
4a = -4
1
4
4a 1
= -4 1
4 4
a = -1
a -1
4 4+ 5a ) = 4 a
4 4+ 5(-1) ) =
4 (-1)
4 -1) ) = -4

47. -4 = -4
-1
4 4+ 5a ) = 4 a
32
3
1) =
=
4
4 = 4
2x = x - 2
-x
2x +(-x) = x -
2+(-x)

48. x = -2
x -2
=
=
-1 = -1
-1 =
33
2) - = 2
- = 2
- = 2
= 2

49. 12
12 = 2 12
x = 24
x 24
- = 2
- = 2
8- 6 = 2
24 - =
2
34

50. 3) + = 20
+ = 20
+ = 20
= 20
= 20
x = 24
x 24
+ = 20
+ = 20
8 + 12 = 20
24 + =
20

51. 4) = + 24
= + 24
- )
+ - ) = + 24 + - )
- = 24
= 24
× = 24 ×
x=
x = 90

52. x 90
= + 24
= +
24
54 = 54
= +
24
35

53. 36
2553).
2
1
2551. :

54. 2549).
2
1
2544. 5. :
. 2545).
1.
:
. (2535). 1
101 1.
:
2542).
:
( . . .). .1-2-
3 &
2544
. :
. (2547). .1
2 2

55. . . 2544. :
3 ( 1- 3)
2 2 1. :
( ).
1 2
2551. 2.
:
2550).
: