# Solve for y 1/2+3/8y=5/12+5/8y 12+38y=512+58y
Combine 38 and y.
12+3y8=512+58y
Combine 58 and y.
12+3y8=512+5y8
Move all terms containing y to the left side of the equation.
Subtract 5y8 from both sides of the equation.
12+3y8-5y8=512
Combine fractions with similar denominators.
12+3y-5y8=512
Subtract 5y from 3y.
12+-2y8=512
Reduce the expression -2y8 by cancelling the common factors.
Factor 2 out of -2y.
12+2(-y)8=512
Factor 2 out of 8.
12+2(-y)2(4)=512
Cancel the common factor.
12+2(-y)2⋅4=512
Rewrite the expression.
12+-y4=512
12+-y4=512
Move the negative in front of the fraction.
12-y4=512
12-y4=512
Move all terms not containing y to the right side of the equation.
Subtract 12 from both sides of the equation.
-y4=512-12
To write -12 as a fraction with a common denominator, multiply by 66.
-y4=512-12⋅66
Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.
Multiply 12 and 66.
-y4=512-62⋅6
Multiply 2 by 6.
-y4=512-612
-y4=512-612
Combine the numerators over the common denominator.
-y4=5-612
Subtract 6 from 5.
-y4=-112
Move the negative in front of the fraction.
-y4=-112
-y4=-112
Multiply both sides of the equation by -4.
-4⋅(-y4)=-4⋅(-112)
Simplify both sides of the equation.
Simplify -4⋅(-y4).
Cancel the common factor of 4.
Move the leading negative in -y4 into the numerator.
-4⋅-y4=-4⋅(-112)
Factor 4 out of -4.
4(-1)⋅-y4=-4⋅(-112)
Cancel the common factor.
4⋅-1⋅-y4=-4⋅(-112)
Rewrite the expression.
-1⋅(-y)=-4⋅(-112)
-1⋅(-y)=-4⋅(-112)
Multiply.
Multiply -1 by -1.
1⋅y=-4⋅(-112)
Multiply y by 1.
y=-4⋅(-112)
y=-4⋅(-112)
y=-4⋅(-112)
Simplify -4⋅(-112).
Cancel the common factor of 4.
Move the leading negative in -112 into the numerator.
y=-4⋅-112
Factor 4 out of -4.
y=4(-1)⋅-112
Factor 4 out of 12.
y=4⋅-1⋅-14⋅3
Cancel the common factor.
y=4⋅-1⋅-14⋅3
Rewrite the expression.
y=-1⋅-13
y=-1⋅-13
Move the negative in front of the fraction.
y=-1⋅(-13)
Multiply -1(-13).
Multiply -1 by -1.
y=1(13)
Multiply 13 by 1.
y=13
y=13
y=13
y=13
The result can be shown in multiple forms.
Exact Form:
y=13
Decimal Form:
y=0.3‾
Solve for y 1/2+3/8y=5/12+5/8y

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