# Solve for y 5/3y+4/5=y-7/3

53y+45=y-73
Combine 53 and y.
5y3+45=y-73
Move all terms containing y to the left side of the equation.
Subtract y from both sides of the equation.
5y3+45-y=-73
To write -y as a fraction with a common denominator, multiply by 33.
5y3-y⋅33+45=-73
Combine -y and 33.
5y3+-y⋅33+45=-73
Combine the numerators over the common denominator.
5y-y⋅33+45=-73
Simplify each term.
Simplify the numerator.
Factor y out of 5y-y⋅3.
Factor y out of 5y.
y⋅5-y⋅33+45=-73
Factor y out of -y⋅3.
y⋅5+y(-1⋅3)3+45=-73
Factor y out of y⋅5+y(-1⋅3).
y(5-1⋅3)3+45=-73
y(5-1⋅3)3+45=-73
Multiply -1 by 3.
y(5-3)3+45=-73
Subtract 3 from 5.
y⋅23+45=-73
y⋅23+45=-73
Move 2 to the left of y.
2y3+45=-73
2y3+45=-73
2y3+45=-73
Move all terms not containing y to the right side of the equation.
Subtract 45 from both sides of the equation.
2y3=-73-45
To write -73 as a fraction with a common denominator, multiply by 55.
2y3=-73⋅55-45
To write -45 as a fraction with a common denominator, multiply by 33.
2y3=-73⋅55-45⋅33
Write each expression with a common denominator of 15, by multiplying each by an appropriate factor of 1.
Multiply 73 and 55.
2y3=-7⋅53⋅5-45⋅33
Multiply 3 by 5.
2y3=-7⋅515-45⋅33
Multiply 45 and 33.
2y3=-7⋅515-4⋅35⋅3
Multiply 5 by 3.
2y3=-7⋅515-4⋅315
2y3=-7⋅515-4⋅315
Combine the numerators over the common denominator.
2y3=-7⋅5-4⋅315
Simplify the numerator.
Multiply -7 by 5.
2y3=-35-4⋅315
Multiply -4 by 3.
2y3=-35-1215
Subtract 12 from -35.
2y3=-4715
2y3=-4715
Move the negative in front of the fraction.
2y3=-4715
2y3=-4715
Multiply both sides of the equation by 32.
32⋅2y3=32⋅(-4715)
Simplify both sides of the equation.
Simplify 32⋅2y3.
Cancel the common factor of 3.
Cancel the common factor.
32⋅2y3=32⋅(-4715)
Rewrite the expression.
12⋅(2y)=32⋅(-4715)
12⋅(2y)=32⋅(-4715)
Cancel the common factor of 2.
Factor 2 out of 2y.
12⋅(2(y))=32⋅(-4715)
Cancel the common factor.
12⋅(2y)=32⋅(-4715)
Rewrite the expression.
y=32⋅(-4715)
y=32⋅(-4715)
y=32⋅(-4715)
Simplify 32⋅(-4715).
Cancel the common factor of 3.
Move the leading negative in -4715 into the numerator.
y=32⋅-4715
Factor 3 out of 15.
y=32⋅-473(5)
Cancel the common factor.
y=32⋅-473⋅5
Rewrite the expression.
y=12⋅-475
y=12⋅-475
Multiply 12 and -475.
y=-472⋅5
Simplify the expression.
Multiply 2 by 5.
y=-4710
Move the negative in front of the fraction.
y=-4710
y=-4710
y=-4710
y=-4710
The result can be shown in multiple forms.
Exact Form:
y=-4710
Decimal Form:
y=-4.7
Mixed Number Form:
y=-4710
Solve for y 5/3y+4/5=y-7/3

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