# Solve for y -1/2y-6/7=-1/3

-12y-67=-13
Combine y and 12.
-y2-67=-13
Move all terms not containing y to the right side of the equation.
Add 67 to both sides of the equation.
-y2=-13+67
To write -13 as a fraction with a common denominator, multiply by 77.
-y2=-13⋅77+67
To write 67 as a fraction with a common denominator, multiply by 33.
-y2=-13⋅77+67⋅33
Write each expression with a common denominator of 21, by multiplying each by an appropriate factor of 1.
Multiply 13 and 77.
-y2=-73⋅7+67⋅33
Multiply 3 by 7.
-y2=-721+67⋅33
Multiply 67 and 33.
-y2=-721+6⋅37⋅3
Multiply 7 by 3.
-y2=-721+6⋅321
-y2=-721+6⋅321
Combine the numerators over the common denominator.
-y2=-7+6⋅321
Simplify the numerator.
Multiply 6 by 3.
-y2=-7+1821
Add -7 and 18.
-y2=1121
-y2=1121
-y2=1121
Multiply both sides of the equation by -2.
-2⋅(-y2)=-2⋅1121
Simplify both sides of the equation.
Simplify -2⋅(-y2).
Cancel the common factor of 2.
Move the leading negative in -y2 into the numerator.
-2⋅-y2=-2⋅1121
Factor 2 out of -2.
2(-1)⋅-y2=-2⋅1121
Cancel the common factor.
2⋅-1⋅-y2=-2⋅1121
Rewrite the expression.
-1⋅(-y)=-2⋅1121
-1⋅(-y)=-2⋅1121
Multiply.
Multiply -1 by -1.
1⋅y=-2⋅1121
Multiply y by 1.
y=-2⋅1121
y=-2⋅1121
y=-2⋅1121
Simplify -2⋅1121.
Multiply -2(1121).
Combine -2 and 1121.
y=-2⋅1121
Multiply -2 by 11.
y=-2221
y=-2221
Move the negative in front of the fraction.
y=-2221
y=-2221
y=-2221
The result can be shown in multiple forms.
Exact Form:
y=-2221
Decimal Form:
y=-1.047619‾
Mixed Number Form:
y=-1121
Solve for y -1/2y-6/7=-1/3

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