# Solve for n (n-11)/4+(n+2)/9=13/18 n-114+n+29=1318
Factor the equation.
To write n-114 as a fraction with a common denominator, multiply by 99.
n-114⋅99+n+29=1318
To write n+29 as a fraction with a common denominator, multiply by 44.
n-114⋅99+n+29⋅44=1318
Write each expression with a common denominator of 36, by multiplying each by an appropriate factor of 1.
Multiply n-114 and 99.
(n-11)⋅94⋅9+n+29⋅44=1318
Multiply 4 by 9.
(n-11)⋅936+n+29⋅44=1318
Multiply n+29 and 44.
(n-11)⋅936+(n+2)⋅49⋅4=1318
Multiply 9 by 4.
(n-11)⋅936+(n+2)⋅436=1318
(n-11)⋅936+(n+2)⋅436=1318
Combine the numerators over the common denominator.
(n-11)⋅9+(n+2)⋅436=1318
Rewrite (n-11)⋅9+(n+2)⋅436 in a factored form.
Apply the distributive property.
n⋅9-11⋅9+(n+2)⋅436=1318
Move 9 to the left of n.
9⋅n-11⋅9+(n+2)⋅436=1318
Multiply -11 by 9.
9n-99+(n+2)⋅436=1318
Apply the distributive property.
9n-99+n⋅4+2⋅436=1318
Move 4 to the left of n.
9n-99+4⋅n+2⋅436=1318
Multiply 2 by 4.
9n-99+4n+836=1318
13n-99+836=1318
13n-9136=1318
Factor 13 out of 13n-91.
Factor 13 out of 13n.
13(n)-9136=1318
Factor 13 out of -91.
13n+13⋅-736=1318
Factor 13 out of 13n+13⋅-7.
13(n-7)36=1318
13(n-7)36=1318
13(n-7)36=1318
13(n-7)36=1318
Solve the equation.
Multiply both sides of the equation by 36.
13(n-7)=1318⋅(36)
Simplify 13(n-7).
Apply the distributive property.
13n+13⋅-7=1318⋅(36)
Multiply 13 by -7.
13n-91=1318⋅(36)
13n-91=1318⋅(36)
Simplify 1318⋅(36).
Cancel the common factor of 18.
Factor 18 out of 36.
13n-91=1318⋅(18(2))
Cancel the common factor.
13n-91=1318⋅(18⋅2)
Rewrite the expression.
13n-91=13⋅2
13n-91=13⋅2
Multiply 13 by 2.
13n-91=26
13n-91=26
Move all terms not containing n to the right side of the equation.
Add 91 to both sides of the equation.
13n=26+91
13n=117
13n=117
Divide each term by 13 and simplify.
Divide each term in 13n=117 by 13.
13n13=11713
Cancel the common factor of 13.
Cancel the common factor.
13n13=11713
Divide n by 1.
n=11713
n=11713
Divide 117 by 13.
n=9
n=9
n=9
Solve for n (n-11)/4+(n+2)/9=13/18     