# Solve for y 5/2y-1/3=-1/2

52y-13=-12
Combine 52 and y.
5y2-13=-12
Move all terms not containing y to the right side of the equation.
Add 13 to both sides of the equation.
5y2=-12+13
To write -12 as a fraction with a common denominator, multiply by 33.
5y2=-12⋅33+13
To write 13 as a fraction with a common denominator, multiply by 22.
5y2=-12⋅33+13⋅22
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
Multiply 12 and 33.
5y2=-32⋅3+13⋅22
Multiply 2 by 3.
5y2=-36+13⋅22
Multiply 13 and 22.
5y2=-36+23⋅2
Multiply 3 by 2.
5y2=-36+26
5y2=-36+26
Combine the numerators over the common denominator.
5y2=-3+26
Add -3 and 2.
5y2=-16
Move the negative in front of the fraction.
5y2=-16
5y2=-16
Multiply both sides of the equation by 25.
25⋅5y2=25⋅(-16)
Simplify both sides of the equation.
Simplify 25⋅5y2.
Cancel the common factor of 2.
Cancel the common factor.
25⋅5y2=25⋅(-16)
Rewrite the expression.
15⋅(5y)=25⋅(-16)
15⋅(5y)=25⋅(-16)
Cancel the common factor of 5.
Factor 5 out of 5y.
15⋅(5(y))=25⋅(-16)
Cancel the common factor.
15⋅(5y)=25⋅(-16)
Rewrite the expression.
y=25⋅(-16)
y=25⋅(-16)
y=25⋅(-16)
Simplify 25⋅(-16).
Cancel the common factor of 2.
Move the leading negative in -16 into the numerator.
y=25⋅-16
Factor 2 out of 6.
y=25⋅-12(3)
Cancel the common factor.
y=25⋅-12⋅3
Rewrite the expression.
y=15⋅-13
y=15⋅-13
Multiply 15 and -13.
y=-15⋅3
Simplify the expression.
Multiply 5 by 3.
y=-115
Move the negative in front of the fraction.
y=-115
y=-115
y=-115
y=-115
The result can be shown in multiple forms.
Exact Form:
y=-115
Decimal Form:
y=-0.06‾
Solve for y 5/2y-1/3=-1/2

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