# Solve for b (b-1)/5+1/6=5/2 b-15+16=52
Simplify b-15+16.
To write b-15 as a fraction with a common denominator, multiply by 66.
b-15⋅66+16=52
To write 16 as a fraction with a common denominator, multiply by 55.
b-15⋅66+16⋅55=52
Write each expression with a common denominator of 30, by multiplying each by an appropriate factor of 1.
Multiply b-15 and 66.
(b-1)⋅65⋅6+16⋅55=52
Multiply 5 by 6.
(b-1)⋅630+16⋅55=52
Multiply 16 and 55.
(b-1)⋅630+56⋅5=52
Multiply 6 by 5.
(b-1)⋅630+530=52
(b-1)⋅630+530=52
Combine the numerators over the common denominator.
(b-1)⋅6+530=52
Simplify the numerator.
Apply the distributive property.
b⋅6-1⋅6+530=52
Move 6 to the left of b.
6⋅b-1⋅6+530=52
Multiply -1 by 6.
6⋅b-6+530=52
6b-130=52
6b-130=52
6b-130=52
Multiply both sides of the equation by 30.
6b-1=52⋅(30)
Remove parentheses.
6b-1=52⋅(30)
Simplify 52⋅(30).
Cancel the common factor of 2.
Factor 2 out of 30.
6b-1=52⋅(2(15))
Cancel the common factor.
6b-1=52⋅(2⋅15)
Rewrite the expression.
6b-1=5⋅15
6b-1=5⋅15
Multiply 5 by 15.
6b-1=75
6b-1=75
Move all terms not containing b to the right side of the equation.
Add 1 to both sides of the equation.
6b=75+1
6b=76
6b=76
Divide each term by 6 and simplify.
Divide each term in 6b=76 by 6.
6b6=766
Cancel the common factor of 6.
Cancel the common factor.
6b6=766
Divide b by 1.
b=766
b=766
Cancel the common factor of 76 and 6.
Factor 2 out of 76.
b=2(38)6
Cancel the common factors.
Factor 2 out of 6.
b=2⋅382⋅3
Cancel the common factor.
b=2⋅382⋅3
Rewrite the expression.
b=383
b=383
b=383
b=383
The result can be shown in multiple forms.
Exact Form:
b=383
Decimal Form:
b=12.6‾
Mixed Number Form:
b=1223
Solve for b (b-1)/5+1/6=5/2

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