Solve for y 4/5y+1/4*(y-5)=(y+1)/5

Math
45y+14⋅(y-5)=y+15
Move y+15 to the left side of the equation by subtracting it from both sides.
45y+14⋅(y-5)-y+15=0
Simplify 45y+14⋅(y-5)-y+15.
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Find the common denominator.
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Write 45y as a fraction with denominator 1.
45y1+14⋅(y-5)-y+15=0
Multiply 45y1 by 55.
45y1⋅55+14⋅(y-5)-y+15=0
Multiply 45y1 and 55.
45y⋅55+14⋅(y-5)-y+15=0
Write 14⋅(y-5) as a fraction with denominator 1.
45y⋅55+14⋅(y-5)1-y+15=0
Multiply 14⋅(y-5)1 by 55.
45y⋅55+14⋅(y-5)1⋅55-y+15=0
Multiply 14⋅(y-5)1 and 55.
45y⋅55+14⋅(y-5)⋅55-y+15=0
45y⋅55+14⋅(y-5)⋅55-y+15=0
Combine the numerators over the common denominator.
45y⋅5+14⋅(y-5)⋅5-(y+1)5=0
Simplify the numerator.
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Combine 45 and y.
4y5⋅5+14⋅(y-5)⋅5-(y+1)5=0
Cancel the common factor of 5.
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Cancel the common factor.
4y5⋅5+14⋅(y-5)⋅5-(y+1)5=0
Rewrite the expression.
4y+14⋅(y-5)⋅5-(y+1)5=0
4y+14⋅(y-5)⋅5-(y+1)5=0
Apply the distributive property.
4y+(14y+14⋅-5)⋅5-(y+1)5=0
Combine 14 and y.
4y+(y4+14⋅-5)⋅5-(y+1)5=0
Combine 14 and -5.
4y+(y4+-54)⋅5-(y+1)5=0
Move the negative in front of the fraction.
4y+(y4-54)⋅5-(y+1)5=0
Apply the distributive property.
4y+y4⋅5-54⋅5-(y+1)5=0
Combine y4 and 5.
4y+y⋅54-54⋅5-(y+1)5=0
Multiply -54⋅5.
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Multiply 5 by -1.
4y+y⋅54-5(54)-(y+1)5=0
Combine -5 and 54.
4y+y⋅54+-5⋅54-(y+1)5=0
Multiply -5 by 5.
4y+y⋅54+-254-(y+1)5=0
4y+y⋅54+-254-(y+1)5=0
Simplify each term.
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Move 5 to the left of y.
4y+5⋅y4+-254-(y+1)5=0
Move the negative in front of the fraction.
4y+5y4-254-(y+1)5=0
4y+5y4-254-(y+1)5=0
Apply the distributive property.
4y+5y4-254-y-1⋅15=0
Multiply -1 by 1.
4y+5y4-254-y-15=0
To write 4y as a fraction with a common denominator, multiply by 44.
4y⋅44+5y4-254-y-15=0
Combine 4y and 44.
4y⋅44+5y4-254-y-15=0
Combine the numerators over the common denominator.
4y⋅4+5y4-254-y-15=0
Combine the numerators over the common denominator.
4y⋅4+5y-254-y-15=0
To write -y as a fraction with a common denominator, multiply by 44.
4y⋅4+5y-254-y⋅44-15=0
Combine -y and 44.
4y⋅4+5y-254+-y⋅44-15=0
Combine the numerators over the common denominator.
4y⋅4+5y-25-y⋅44-15=0
To write -1 as a fraction with a common denominator, multiply by 44.
4y⋅4+5y-25-y⋅44-1⋅445=0
Combine -1 and 44.
4y⋅4+5y-25-y⋅44+-1⋅445=0
Combine the numerators over the common denominator.
4y⋅4+5y-25-y⋅4-1⋅445=0
Reorder terms.
4⋅4y-1⋅4y+5y-25-1⋅445=0
Rewrite 4⋅4y-1⋅4y+5y-25-1⋅44 in a factored form.
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Multiply 4 by 4.
16y-1⋅4y+5y-25-1⋅445=0
Multiply -1 by 4.
16y-4y+5y-25-1⋅445=0
Multiply -1 by 4.
16y-4y+5y-25-445=0
Subtract 4y from 16y.
12y+5y-25-445=0
Add 12y and 5y.
17y-25-445=0
Subtract 4 from -25.
17y-2945=0
17y-2945=0
17y-2945=0
Multiply the numerator by the reciprocal of the denominator.
17y-294⋅15=0
Multiply 17y-294⋅15.
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Multiply 17y-294 and 15.
17y-294⋅5=0
Multiply 4 by 5.
17y-2920=0
17y-2920=0
17y-2920=0
Since this is the only denominator in the list, the result is the LCD: 20.
20
Multiply each term by 20 and simplify.
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Multiply each term in 17y-2920=0 by 20.
17y-2920⋅20=0⋅20
Cancel the common factor of 20.
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Cancel the common factor.
17y-2920⋅20=0⋅20
Rewrite the expression.
17y-29=0⋅20
17y-29=0⋅20
Multiply 0 by 20.
17y-29=0
17y-29=0
Add 29 to both sides of the equation.
17y=29
Divide each term by 17 and simplify.
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Divide each term in 17y=29 by 17.
17y17=2917
Cancel the common factor of 17.
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Cancel the common factor.
17y17=2917
Divide y by 1.
y=2917
y=2917
y=2917
The result can be shown in multiple forms.
Exact Form:
y=2917
Decimal Form:
y=1.70588235…
Mixed Number Form:
y=11217
Solve for y 4/5y+1/4*(y-5)=(y+1)/5

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