# Solve for y (y+1)/4=3/2+(y+9)/7

y+14=32+y+97
Multiply both sides of the equation by 4.
y+1=(32+y+97)⋅(4)
Remove parentheses.
y+1=(32+y+97)⋅(4)
Simplify (32+y+97)⋅(4).
To write 32 as a fraction with a common denominator, multiply by 77.
y+1=(32⋅77+y+97)⋅4
To write y+97 as a fraction with a common denominator, multiply by 22.
y+1=(32⋅77+y+97⋅22)⋅4
Write each expression with a common denominator of 14, by multiplying each by an appropriate factor of 1.
Multiply 32 and 77.
y+1=(3⋅72⋅7+y+97⋅22)⋅4
Multiply 2 by 7.
y+1=(3⋅714+y+97⋅22)⋅4
Multiply y+97 and 22.
y+1=(3⋅714+(y+9)⋅27⋅2)⋅4
Multiply 7 by 2.
y+1=(3⋅714+(y+9)⋅214)⋅4
y+1=(3⋅714+(y+9)⋅214)⋅4
Combine the numerators over the common denominator.
y+1=3⋅7+(y+9)⋅214⋅4
Simplify the numerator.
Multiply 3 by 7.
y+1=21+(y+9)⋅214⋅4
Apply the distributive property.
y+1=21+y⋅2+9⋅214⋅4
Move 2 to the left of y.
y+1=21+2⋅y+9⋅214⋅4
Multiply 9 by 2.
y+1=21+2⋅y+1814⋅4
Add 21 and 18.
y+1=2y+3914⋅4
y+1=2y+3914⋅4
Simplify terms.
Cancel the common factor of 2.
Factor 2 out of 14.
y+1=2y+392(7)⋅4
Factor 2 out of 4.
y+1=2y+392⋅7⋅(2⋅2)
Cancel the common factor.
y+1=2y+392⋅7⋅(2⋅2)
Rewrite the expression.
y+1=2y+397⋅2
y+1=2y+397⋅2
Combine 2y+397 and 2.
y+1=(2y+39)⋅27
Move 2 to the left of 2y+39.
y+1=2(2y+39)7
y+1=2(2y+39)7
y+1=2(2y+39)7
Move all terms containing y to the left side of the equation.
Subtract 2(2y+39)7 from both sides of the equation.
y+1-2(2y+39)7=0
To write y as a fraction with a common denominator, multiply by 77.
y⋅77-2(2y+39)7+1=0
Combine y and 77.
y⋅77-2(2y+39)7+1=0
Combine the numerators over the common denominator.
y⋅7-2(2y+39)7+1=0
Simplify the numerator.
Move 7 to the left of y.
7⋅y-2(2y+39)7+1=0
Apply the distributive property.
7y-2(2y)-2⋅397+1=0
Multiply 2 by -2.
7y-4y-2⋅397+1=0
Multiply -2 by 39.
7y-4y-787+1=0
Subtract 4y from 7y.
3y-787+1=0
Factor 3 out of 3y-78.
Factor 3 out of 3y.
3(y)-787+1=0
Factor 3 out of -78.
3y+3⋅-267+1=0
Factor 3 out of 3y+3⋅-26.
3(y-26)7+1=0
3(y-26)7+1=0
3(y-26)7+1=0
Write 1 as a fraction with a common denominator.
3(y-26)7+77=0
Combine the numerators over the common denominator.
3(y-26)+77=0
Simplify the numerator.
Apply the distributive property.
3y+3⋅-26+77=0
Multiply 3 by -26.
3y-78+77=0
Add -78 and 7.
3y-717=0
3y-717=0
3y-717=0
Multiply both sides of the equation by 7.
3y-71=0⋅(7)
Remove parentheses.
3y-71=0⋅(7)
Multiply 0 by 7.
3y-71=0
Add 71 to both sides of the equation.
3y=71
Divide each term by 3 and simplify.
Divide each term in 3y=71 by 3.
3y3=713
Cancel the common factor of 3.
Cancel the common factor.
3y3=713
Divide y by 1.
y=713
y=713
y=713
The result can be shown in multiple forms.
Exact Form:
y=713
Decimal Form:
y=23.6‾
Mixed Number Form:
y=2323
Solve for y (y+1)/4=3/2+(y+9)/7

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