Solve for y 1/3y+9=1/10y

Math
13y+9=110y
Combine 13 and y.
y3+9=110y
Combine 110 and y.
y3+9=y10
Move all terms containing y to the left side of the equation.
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Subtract y10 from both sides of the equation.
y3+9-y10=0
To write y3 as a fraction with a common denominator, multiply by 1010.
y3⋅1010-y10+9=0
To write -y10 as a fraction with a common denominator, multiply by 33.
y3⋅1010-y10⋅33+9=0
Write each expression with a common denominator of 30, by multiplying each by an appropriate factor of 1.
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Multiply y3 and 1010.
y⋅103⋅10-y10⋅33+9=0
Multiply 3 by 10.
y⋅1030-y10⋅33+9=0
Multiply y10 and 33.
y⋅1030-y⋅310⋅3+9=0
Multiply 10 by 3.
y⋅1030-y⋅330+9=0
y⋅1030-y⋅330+9=0
Combine the numerators over the common denominator.
y⋅10-y⋅330+9=0
Simplify each term.
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Simplify the numerator.
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Factor y out of y⋅10-y⋅3.
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Factor y out of y⋅10.
y(10)-y⋅330+9=0
Factor y out of -y⋅3.
y(10)+y(-1⋅3)30+9=0
Factor y out of y(10)+y(-1⋅3).
y(10-1⋅3)30+9=0
y(10-1⋅3)30+9=0
Multiply -1 by 3.
y(10-3)30+9=0
Subtract 3 from 10.
y⋅730+9=0
y⋅730+9=0
Move 7 to the left of y.
7y30+9=0
7y30+9=0
7y30+9=0
Subtract 9 from both sides of the equation.
7y30=-9
Multiply both sides of the equation by 307.
307⋅7y30=307⋅-9
Simplify both sides of the equation.
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Simplify 307⋅7y30.
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Cancel the common factor of 30.
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Cancel the common factor.
307⋅7y30=307⋅-9
Rewrite the expression.
17⋅(7y)=307⋅-9
17⋅(7y)=307⋅-9
Cancel the common factor of 7.
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Factor 7 out of 7y.
17⋅(7(y))=307⋅-9
Cancel the common factor.
17⋅(7y)=307⋅-9
Rewrite the expression.
y=307⋅-9
y=307⋅-9
y=307⋅-9
Simplify 307⋅-9.
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Multiply 307⋅-9.
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Combine 307 and -9.
y=30⋅-97
Multiply 30 by -9.
y=-2707
y=-2707
Move the negative in front of the fraction.
y=-2707
y=-2707
y=-2707
The result can be shown in multiple forms.
Exact Form:
y=-2707
Decimal Form:
y=-38.57142857…
Mixed Number Form:
y=-3847
Solve for y 1/3y+9=1/10y

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