Solve for y (3y)/4+(y-2)/3=(2y+1)/2-1

Math
3y4+y-23=2y+12-1
Simplify 3y4+y-23.
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To write 3y4 as a fraction with a common denominator, multiply by 33.
3y4⋅33+y-23=2y+12-1
To write y-23 as a fraction with a common denominator, multiply by 44.
3y4⋅33+y-23⋅44=2y+12-1
Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.
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Multiply 3y4 and 33.
3y⋅34⋅3+y-23⋅44=2y+12-1
Multiply 4 by 3.
3y⋅312+y-23⋅44=2y+12-1
Multiply y-23 and 44.
3y⋅312+(y-2)⋅43⋅4=2y+12-1
Multiply 3 by 4.
3y⋅312+(y-2)⋅412=2y+12-1
3y⋅312+(y-2)⋅412=2y+12-1
Combine the numerators over the common denominator.
3y⋅3+(y-2)⋅412=2y+12-1
Simplify the numerator.
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Multiply 3 by 3.
9y+(y-2)⋅412=2y+12-1
Apply the distributive property.
9y+y⋅4-2⋅412=2y+12-1
Move 4 to the left of y.
9y+4⋅y-2⋅412=2y+12-1
Multiply -2 by 4.
9y+4⋅y-812=2y+12-1
Add 9y and 4y.
13y-812=2y+12-1
13y-812=2y+12-1
13y-812=2y+12-1
Simplify 2y+12-1.
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To write -1 as a fraction with a common denominator, multiply by 22.
13y-812=2y+12-1⋅22
Simplify terms.
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Combine -1 and 22.
13y-812=2y+12+-1⋅22
Combine the numerators over the common denominator.
13y-812=2y+1-1⋅22
13y-812=2y+1-1⋅22
Simplify the numerator.
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Multiply -1 by 2.
13y-812=2y+1-22
Subtract 2 from 1.
13y-812=2y-12
13y-812=2y-12
13y-812=2y-12
Move all terms containing y to the left side of the equation.
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Subtract 2y-12 from both sides of the equation.
13y-812-2y-12=0
To write -2y-12 as a fraction with a common denominator, multiply by 66.
13y-812-2y-12⋅66=0
Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1.
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Multiply 2y-12 and 66.
13y-812-(2y-1)⋅62⋅6=0
Multiply 2 by 6.
13y-812-(2y-1)⋅612=0
13y-812-(2y-1)⋅612=0
Combine the numerators over the common denominator.
13y-8-(2y-1)⋅612=0
Simplify the numerator.
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Apply the distributive property.
13y-8+(-(2y)–1)⋅612=0
Multiply 2 by -1.
13y-8+(-2y–1)⋅612=0
Multiply -1 by -1.
13y-8+(-2y+1)⋅612=0
Apply the distributive property.
13y-8-2y⋅6+1⋅612=0
Multiply 6 by -2.
13y-8-12y+1⋅612=0
Multiply 6 by 1.
13y-8-12y+612=0
Subtract 12y from 13y.
y-8+612=0
Add -8 and 6.
y-212=0
y-212=0
y-212=0
Multiply both sides of the equation by 12.
12⋅y-212=12⋅0
Simplify both sides of the equation.
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Cancel the common factor of 12.
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Cancel the common factor.
12⋅y-212=12⋅0
Rewrite the expression.
y-2=12⋅0
y-2=12⋅0
Multiply 12 by 0.
y-2=0
y-2=0
Add 2 to both sides of the equation.
y=2
Solve for y (3y)/4+(y-2)/3=(2y+1)/2-1

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