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           ☆1 equations

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    Work: Find the solution of equation 50(1-0.3)(1+3x)×0.3(1－x) = 0 .
    Question type: Equation
    Solution:Original question:

50

(

1

−

3 10

)

(

1

+

3

x

)

×

3 10

(

1

−

x

)

=

0

Left side of the equation =

15

(

1

−

3 10

)

(

1

+

3

x

)

(

1

−

x

)

    The equation is transformed into :

15

(

1

−

3 10

)

(

1

+

3

x

)

(

1

−

x

)

=

0

    Remove the bracket on the left of the equation:

Left side of the equation =

15

×

1

(

1

+

3

x

)

(

1

−

x

)

−

15

×

3 10

(

1

+

3

x

)

(

1

−

x

)

=

15

(

1

+

3

x

)

(

1

−

x

)

−

9 2

(

1

+

3

x

)

(

1

−

x

)

=

15

×

1

(

1

−

x

)

+

15

×

3

x

(

1

−

x

)

−

9 2

(

1

+

3

x

)

(

1

−

x

)

=

15

(

1

−

x

)

+

45

x

(

1

−

x

)

−

9 2

(

1

+

3

x

)

(

1

−

x

)

=

15

×

1

−

15

x

+

45

x

(

1

−

x

)

−

9 2

(

1

+

3

x

)

(

1

−

x

)

=

15

−

15

x

+

45

x

(

1

−

x

)

−

9 2

(

1

+

3

x

)

(

1

−

x

)

=

15

−

15

x

+

45

x

×

1

−

45

x

x

−

9 2

(

1

+

3

x

)

(

1

−

x

)

=

15

−

15

x

+

45

x

−

45

x

x

−

9 2

(

1

+

3

x

)

(

1

−

x

)

=

15

+

30

x

−

45

x

x

−

9 2

(

1

+

3

x

)

(

1

−

x

)

=

15

+

30

x

−

45

x

x

−

9 2

×

1

(

1

−

x

)

−

9 2

×

3

x

=

15

+

30

x

−

45

x

x

−

9 2

(

1

−

x

)

−

27 2

x

(

1

−

x

)

=

15

+

30

x

−

45

x

x

−

9 2

×

1

+

9 2

x

−

27 2

x

=

15

+

30

x

−

45

x

x

−

9 2

+

9 2

x

−

27 2

x

(

1

−

x

)

=

21 2

+

69 2

x

−

45

x

x

−

27 2

x

(

1

−

x

)

=

21 2

+

69 2

x

−

45

x

x

−

27 2

x

×

1

+

27 2

x

x

=

21 2

+

69 2

x

−

45

x

x

−

27 2

x

+

27 2

x

x

=

21 2

+

21

x

−

45

x

x

+

27 2

x

x

    The equation is transformed into :

21 2

+

21

x

−

45

x

x

+

27 2

x

x

=

0

    After the equation is converted into a general formula, it is converted into:
    ( 3x + 1 )( x - 1 )=0
    From
        3x + 1 = 0
        x - 1 = 0
    it is concluded that:：

x1=

-

1 3

x2=1

    
    There are 2 solution(s).

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