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    Work: Find the solution of equation 0.5(-y+10)*4*1-0.5*5*4-0.5(y-5) = 10 .
    Question type: Equation
    Solution:Original question:

1 2

(

-

y

+

10

)

×

4

×

1

−

1 2

×

5

×

4

−

1 2

(

y

−

5

)

=

10

Left side of the equation =

2

(

-

y

+

10

)

−

10

−

1 2

(

y

−

5

)

    The equation is transformed into :

2

(

-

y

+

10

)

−

10

−

1 2

(

y

−

5

)

=

10

    Remove the bracket on the left of the equation:

Left side of the equation =

-

2

y

+

2

×

10

−

10

−

1 2

(

y

−

5

)

=

-

2

y

+

20

−

10

−

1 2

(

y

−

5

)

=

-

2

y

+

10

−

1 2

(

y

−

5

)

=

-

2

y

+

10

−

1 2

y

+

1 2

×

5

=

-

2

y

+

10

−

1 2

y

+

5 2

=

-

5 2

y

+

25 2

    The equation is transformed into :

-

5 2

y

+

25 2

=

10

    Transposition :

-

5 2

y

=

10

−

25 2

    Combine the items on the right of the equation:

-

5 2

y

=

-

5 2

    By shifting the terms and changing the symbols on toth sides of the equation, we obtain :

5 2

=

5 2

y

    If the left side of the equation is equal to the right side, then the right side must also be equal to the left side, that is :

5 2

y

=

5 2

    The coefficient of the unknown number is reduced to 1 :

y

=

5 2

÷

5 2

=

5 2

×

2 5

=

1

×

1

    We obtained :

y

=

1

    This is the solution of the equation.

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