# Solve for y -5/2y-5/3=-1/6y-7/2

-52y-53=-16y-72
Simplify each term.
Combine y and 52.
-y⋅52-53=-16y-72
Move 5 to the left of y.
-5y2-53=-16y-72
-5y2-53=-16y-72
Combine y and 16.
-5y2-53=-y6-72
Move all terms containing y to the left side of the equation.
Add y6 to both sides of the equation.
-5y2-53+y6=-72
To write -5y2 as a fraction with a common denominator, multiply by 33.
-5y2⋅33+y6-53=-72
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
Multiply 5y2 and 33.
-5y⋅32⋅3+y6-53=-72
Multiply 2 by 3.
-5y⋅36+y6-53=-72
-5y⋅36+y6-53=-72
Combine the numerators over the common denominator.
-5y⋅3+y6-53=-72
Simplify each term.
Simplify the numerator.
Factor y out of -5y⋅3+y.
Factor y out of -5y⋅3.
y(-5⋅3)+y6-53=-72
Raise y to the power of 1.
y(-5⋅3)+y16-53=-72
Factor y out of y1.
y(-5⋅3)+y⋅16-53=-72
Factor y out of y(-5⋅3)+y⋅1.
y(-5⋅3+1)6-53=-72
y(-5⋅3+1)6-53=-72
Multiply -5 by 3.
y(-15+1)6-53=-72
Add -15 and 1.
y⋅-146-53=-72
y⋅-146-53=-72
Cancel the common factor of -14 and 6.
Factor 2 out of y⋅-14.
2(y⋅-7)6-53=-72
Cancel the common factors.
Factor 2 out of 6.
2(y⋅-7)2(3)-53=-72
Cancel the common factor.
2(y⋅-7)2⋅3-53=-72
Rewrite the expression.
y⋅-73-53=-72
y⋅-73-53=-72
y⋅-73-53=-72
Move -7 to the left of y.
-7⋅y3-53=-72
Move the negative in front of the fraction.
-7y3-53=-72
-7y3-53=-72
-7y3-53=-72
Move all terms not containing y to the right side of the equation.
Add 53 to both sides of the equation.
-7y3=-72+53
To write -72 as a fraction with a common denominator, multiply by 33.
-7y3=-72⋅33+53
To write 53 as a fraction with a common denominator, multiply by 22.
-7y3=-72⋅33+53⋅22
Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.
Multiply 72 and 33.
-7y3=-7⋅32⋅3+53⋅22
Multiply 2 by 3.
-7y3=-7⋅36+53⋅22
Multiply 53 and 22.
-7y3=-7⋅36+5⋅23⋅2
Multiply 3 by 2.
-7y3=-7⋅36+5⋅26
-7y3=-7⋅36+5⋅26
Combine the numerators over the common denominator.
-7y3=-7⋅3+5⋅26
Simplify the numerator.
Multiply -7 by 3.
-7y3=-21+5⋅26
Multiply 5 by 2.
-7y3=-21+106
Add -21 and 10.
-7y3=-116
-7y3=-116
Move the negative in front of the fraction.
-7y3=-116
-7y3=-116
Multiply both sides of the equation by -37.
-37⋅(-7y3)=-37⋅(-116)
Simplify both sides of the equation.
Simplify -37⋅(-7y3).
Cancel the common factor of 3.
Move the leading negative in -37 into the numerator.
-37⋅(-7y3)=-37⋅(-116)
Move the leading negative in -7y3 into the numerator.
-37⋅-7y3=-37⋅(-116)
Factor 3 out of -3.
3(-1)7⋅-7y3=-37⋅(-116)
Cancel the common factor.
3⋅-17⋅-7y3=-37⋅(-116)
Rewrite the expression.
-17⋅(-7y)=-37⋅(-116)
-17⋅(-7y)=-37⋅(-116)
Cancel the common factor of 7.
Factor 7 out of -7y.
-17⋅(7(-y))=-37⋅(-116)
Cancel the common factor.
-17⋅(7(-y))=-37⋅(-116)
Rewrite the expression.
-1⋅(-y)=-37⋅(-116)
-1⋅(-y)=-37⋅(-116)
Multiply.
Multiply -1 by -1.
1⋅y=-37⋅(-116)
Multiply y by 1.
y=-37⋅(-116)
y=-37⋅(-116)
y=-37⋅(-116)
Simplify -37⋅(-116).
Cancel the common factor of 3.
Move the leading negative in -37 into the numerator.
y=-37⋅(-116)
Move the leading negative in -116 into the numerator.
y=-37⋅-116
Factor 3 out of -3.
y=3(-1)7⋅-116
Factor 3 out of 6.
y=3⋅-17⋅-113⋅2
Cancel the common factor.
y=3⋅-17⋅-113⋅2
Rewrite the expression.
y=-17⋅-112
y=-17⋅-112
Multiply -17 and -112.
y=–117⋅2
Multiply.
Multiply -1 by -11.
y=117⋅2
Multiply 7 by 2.
y=1114
y=1114
y=1114
y=1114
The result can be shown in multiple forms.
Exact Form:
y=1114
Decimal Form:
y=0.7857142‾
Solve for y -5/2y-5/3=-1/6y-7/2

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