2145-1.2 Proto a.doc

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3

1.2 . 20-21

1.

) 5 + = 35 ) 5 ( ..= 35 ) 127 = 103) 32 = 35 ) 14 + . = 5 ) 2 ( ..+ 3 =17

) x , 5 + x = 35 x = 35 5

x = 30) x , 5x = 35 x =

x = 7) x , 127x = 103 x = 127103

x = 24

) x , 32x = 35 x = 32 35

x = 3

) x , 14 + x = 5 x = 5 14

x = 9

) x , 2 (x + 3 = 17 2x = 17 3 2x = 14 x = 7

) 5 + 30 = 35 ) 5 ( 7 = 35 ) 127 24 = 103) 32( 3) = 35 ) 14 + (9) = 5 ) 2 (7 + 3 = 17

2.

() ()

) 2x = 6 3

) 2x + x = x

) x + 1= 5 x + 5 = 1

) 3x = 0 ) 0x = 0

) 2( 3 = 6, 3 ()

) 2x + x = x 2x = 0 x = 0. 0, .

() ) x + 1= 5 x = 5 1 = 4 x + 5 = 1 x = 15 x = 4 x = 4 4, () ) 3x = 0 x = = 0, 0, , ()

) x, . () 3.

.

) 2x = 4 i) 8

) 3x = 9ii) 3

) x = 4iii) 2

) 2x = 3 + xi) 3

) 2x = 4 x = = 2 ) 3x = 9 x = = 3

) x = 4 x = 4 (2 = 8 ) 2x = 3 + x 2x x = 3 x = 3 ( iii ( i ( i ( ii

1.

) 2x + 3 = 21 x = 7

) 3x + 5 = 7,5 x = 0,5

) 3x + 4 = 7x 6 x = 1 ) x 7 2( 7) + 3 = 21 14 + 3 = 21 17 = 21

7

)

x 0,5 3(0,5 + 5 = 7,5

1,5 + 5 = 7,5 6,5 = 7,5

0,5 ) x 1 3(1 + 4 = 7(16 3 + 4 = 7 6 1= 1

1 2.

) 2x + 21 = 4 + x 5

) 9 + 7y + y =1 2y

) 3t 3( t + 1) = t + 2( t + 1) + 1 ) 2x + 21 = 4 + x 5 2x x = 4 5 21 x = 22

) 9 + 7y + y =1 2y 7y + y + 2y =1 + 9 10y = 10 y = = 1 ) 3t 3( t + 1) = t + 2( t + 1) + 1 3t3t 3 = t + 2t + 2 + 1

3t3t t2t = 2 + 1 + 3 3t = 6 t = = 2

3.

) 4( 2x + 1) 6(x 1) = 3( x + 2)

) 3(y + 1) + 2( y 4) =2y (y 6)

) 6( + 2) + 3 = 3 2( 4) ) 4( 2x + 1) 6(x 1) = 3( x + 2)

8x + 4 6x + 6 = 3x + 6

8x 6x 3x = 664

x = 4 x = 4

) 3(y + 1) + 2( y 4) =2y (y 6)

3y + 3 + 2y 8 = 2yy + 6

3y + 2y 2y + y = 6 + 8 3

4y = 11 y = ) 6( + 2) + 3 = 3 2( 4) 6 + 12 + 3 = 32 + 8

6 + 2 = 3 + 8 123

8 = 4 = =

4 .

) =

) =

) =

) = 4( = 4 (

2( 2x + 3) = 1(3x5)

4x + 6 = 3x5

4x 3x = 56 x = 11

) = 12( =12(

4( 7x6) = 3(5x + 2)

28x24 = 15x + 6

28x15x = 6 + 24

13 x = 30 x =

) = 4(= 4(

2([2(x1) 2] = 1(13x)

2(2x22) = 13x 4x44 = 13x 4x + 3x = 1 + 4 + 4

7x = 9 x =

5.

) = 2 ) = y +

) ( + 4) 7 = (1 ) +

)

= 2 15( 15( = 15( 15(2 3(x + 4) 5( x4) = 1(13x) 30

3x + 12 5x + 20 = 13x 30

3x5x + 3x = 1301220

x = 61

)

= y + 6( 6( = 6y + 6(

2(y1) 1(2y + 7) = 6y + 3(13y)

2y22y7 = 6y + 39y 2y2y + 9y6y = 3 + 2 + 7

3y = 12 y = = 4 )

( + 4) 7 = (1 ) + + 1 7 =

+

28( + 28( 1 28(7 =28(

28( + 28(

7 + 28 196 = 4 4 + 7( 23)

7 + 28 196 = 4 4 + 7161

7 + 4 7 = 4161 28 + 196

4 = 11 =

6.

) 3x = 6 ) 5 = 12

) 3x = 6 3x + 5 = 6 + 2 3(3x3( + 3 (5 = 3( 6 3( + 3(2

9x 2x + 15 = 18 x + 6

9x2x + x = 18 + 6 15

8x = 9 x =

) 5 = 12 5

= 12 t +

6(56( 6( = 6(12 6t + 6(

30 3( t + 1) 2( 1 + 2t) = 72 6t + 1( t + 5)

30 3t3 24t = 72 6t + t + 5

3t4t + 6tt = 72 + 5 30 + 3 + 2

2t = 52

t = = 267.

) = ) =

)

= 3( = 1( = 1 +

4( = 4(1 + 4(

2( 3x + 3) = 4 + 1

6x + 6= 5

6x = 56 6x = 1 x =

)

= =

=

EMBED Equation.DSMT4 =

EMBED Equation.DSMT4

3t

=

4 (3t 4( = 4( 4( 12t2 = 105t 12t + 5t = 10 + 2

17t = 12 t =

8.

x =

) = 5x 3 , B = 122x) A = 2(x 1) + , B = 6 +

) = 5x 3 = 122x 5x + 2x = 12 + 3

7x = 15 x =

) = 2(x1) + = 6 +

6(2(x1) + 6( = 6( 6 + 6(

12(x1) + 9 = 36 + 2x 12x 12 + 9 = 36 + 2x 12x2x = 36 + 129

10x = 39 x = = 3,9 9.

( x + 6) 2 = ( 2 1)x + 2

) = 2, x = 8 ) x = 7, = 3

) = 1,

) = 2 2( x