# Solve for y 1/4y-7/8y=10-45

14y-78y=10-45
Simplify 14y-78y.
Simplify each term.
Combine 14 and y.
y4-78y=10-45
Combine y and 78.
y4-y⋅78=10-45
Move 7 to the left of y.
y4-7y8=10-45
y4-7y8=10-45
To write y4 as a fraction with a common denominator, multiply by 22.
y4⋅22-7y8=10-45
Write each expression with a common denominator of 8, by multiplying each by an appropriate factor of 1.
Multiply y4 and 22.
y⋅24⋅2-7y8=10-45
Multiply 4 by 2.
y⋅28-7y8=10-45
y⋅28-7y8=10-45
Combine the numerators over the common denominator.
y⋅2-7y8=10-45
Simplify the numerator.
Move 2 to the left of y.
2⋅y-7y8=10-45
Subtract 7y from 2y.
-5y8=10-45
-5y8=10-45
Move the negative in front of the fraction.
-5y8=10-45
-5y8=10-45
Subtract 45 from 10.
-5y8=-35
Multiply both sides of the equation by -85.
-85⋅(-5y8)=-85⋅-35
Simplify both sides of the equation.
Simplify -85⋅(-5y8).
Cancel the common factor of 8.
Move the leading negative in -85 into the numerator.
-85⋅(-5y8)=-85⋅-35
Move the leading negative in -5y8 into the numerator.
-85⋅-5y8=-85⋅-35
Factor 8 out of -8.
8(-1)5⋅-5y8=-85⋅-35
Cancel the common factor.
8⋅-15⋅-5y8=-85⋅-35
Rewrite the expression.
-15⋅(-5y)=-85⋅-35
-15⋅(-5y)=-85⋅-35
Cancel the common factor of 5.
Factor 5 out of -5y.
-15⋅(5(-y))=-85⋅-35
Cancel the common factor.
-15⋅(5(-y))=-85⋅-35
Rewrite the expression.
-1⋅(-y)=-85⋅-35
-1⋅(-y)=-85⋅-35
Multiply.
Multiply -1 by -1.
1⋅y=-85⋅-35
Multiply y by 1.
y=-85⋅-35
y=-85⋅-35
y=-85⋅-35
Simplify -85⋅-35.
Cancel the common factor of 5.
Move the leading negative in -85 into the numerator.
y=-85⋅-35
Factor 5 out of -35.
y=-85⋅(5(-7))
Cancel the common factor.
y=-85⋅(5⋅-7)
Rewrite the expression.
y=-8⋅-7
y=-8⋅-7
Multiply -8 by -7.
y=56
y=56
y=56
Solve for y 1/4y-7/8y=10-45

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