# Solve for y -1/2-3/4y=5/3 -12-34y=53
Simplify each term.
Combine y and 34.
-12-y⋅34=53
Move 3 to the left of y.
-12-3y4=53
-12-3y4=53
Move all terms not containing y to the right side of the equation.
Add 12 to both sides of the equation.
-3y4=53+12
To write 53 as a fraction with a common denominator, multiply by 22.
-3y4=53⋅22+12
To write 12 as a fraction with a common denominator, multiply by 33.
-3y4=53⋅22+12⋅33
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
Multiply 53 and 22.
-3y4=5⋅23⋅2+12⋅33
Multiply 3 by 2.
-3y4=5⋅26+12⋅33
Multiply 12 and 33.
-3y4=5⋅26+32⋅3
Multiply 2 by 3.
-3y4=5⋅26+36
-3y4=5⋅26+36
Combine the numerators over the common denominator.
-3y4=5⋅2+36
Simplify the numerator.
Multiply 5 by 2.
-3y4=10+36
Add 10 and 3.
-3y4=136
-3y4=136
-3y4=136
Multiply both sides of the equation by -43.
-43⋅(-3y4)=-43⋅136
Simplify both sides of the equation.
Simplify -43⋅(-3y4).
Cancel the common factor of 4.
Move the leading negative in -43 into the numerator.
-43⋅(-3y4)=-43⋅136
Move the leading negative in -3y4 into the numerator.
-43⋅-3y4=-43⋅136
Factor 4 out of -4.
4(-1)3⋅-3y4=-43⋅136
Cancel the common factor.
4⋅-13⋅-3y4=-43⋅136
Rewrite the expression.
-13⋅(-3y)=-43⋅136
-13⋅(-3y)=-43⋅136
Cancel the common factor of 3.
Factor 3 out of -3y.
-13⋅(3(-y))=-43⋅136
Cancel the common factor.
-13⋅(3(-y))=-43⋅136
Rewrite the expression.
-1⋅(-y)=-43⋅136
-1⋅(-y)=-43⋅136
Multiply.
Multiply -1 by -1.
1⋅y=-43⋅136
Multiply y by 1.
y=-43⋅136
y=-43⋅136
y=-43⋅136
Simplify -43⋅136.
Cancel the common factor of 2.
Move the leading negative in -43 into the numerator.
y=-43⋅136
Factor 2 out of -4.
y=2(-2)3⋅136
Factor 2 out of 6.
y=2⋅-23⋅132⋅3
Cancel the common factor.
y=2⋅-23⋅132⋅3
Rewrite the expression.
y=-23⋅133
y=-23⋅133
Multiply -23 and 133.
y=-2⋅133⋅3
Simplify the expression.
Multiply -2 by 13.
y=-263⋅3
Multiply 3 by 3.
y=-269
Move the negative in front of the fraction.
y=-269
y=-269
y=-269
y=-269
The result can be shown in multiple forms.
Exact Form:
y=-269
Decimal Form:
y=-2.8‾
Mixed Number Form:
y=-289
Solve for y -1/2-3/4y=5/3

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