Solve for y (y+4)/5=(y-2)/3

y+45=y-23
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
(y+4)⋅3=5⋅(y-2)
Solve the equation for y.
Simplify (y+4)⋅3.
Apply the distributive property.
y⋅3+4⋅3=5⋅(y-2)
Simplify the expression.
Move 3 to the left of y.
3⋅y+4⋅3=5⋅(y-2)
Multiply 4 by 3.
3y+12=5⋅(y-2)
3y+12=5⋅(y-2)
3y+12=5⋅(y-2)
Simplify 5⋅(y-2).
Apply the distributive property.
3y+12=5y+5⋅-2
Multiply 5 by -2.
3y+12=5y-10
3y+12=5y-10
Move all terms containing y to the left side of the equation.
Subtract 5y from both sides of the equation.
3y+12-5y=-10
Subtract 5y from 3y.
-2y+12=-10
-2y+12=-10
Move all terms not containing y to the right side of the equation.
Subtract 12 from both sides of the equation.
-2y=-10-12
Subtract 12 from -10.
-2y=-22
-2y=-22
Divide each term by -2 and simplify.
Divide each term in -2y=-22 by -2.
-2y-2=-22-2
Cancel the common factor of -2.
Cancel the common factor.
-2y-2=-22-2
Divide y by 1.
y=-22-2
y=-22-2
Divide -22 by -2.
y=11
y=11
y=11
Solve for y (y+4)/5=(y-2)/3

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