# Solve for c 4/5c-7=1/10c

45c-7=110c
Combine 45 and c.
4c5-7=110c
Combine 110 and c.
4c5-7=c10
Move all terms containing c to the left side of the equation.
Subtract c10 from both sides of the equation.
4c5-7-c10=0
To write 4c5 as a fraction with a common denominator, multiply by 22.
4c5⋅22-c10-7=0
Write each expression with a common denominator of 10, by multiplying each by an appropriate factor of 1.
Multiply 4c5 and 22.
4c⋅25⋅2-c10-7=0
Multiply 5 by 2.
4c⋅210-c10-7=0
4c⋅210-c10-7=0
Combine the numerators over the common denominator.
4c⋅2-c10-7=0
Simplify each term.
Simplify the numerator.
Factor c out of 4c⋅2-c.
Factor c out of 4c⋅2.
c(4⋅2)-c10-7=0
Factor c out of -c.
c(4⋅2)+c⋅-110-7=0
Factor c out of c(4⋅2)+c⋅-1.
c(4⋅2-1)10-7=0
c(4⋅2-1)10-7=0
Multiply 4 by 2.
c(8-1)10-7=0
Subtract 1 from 8.
c⋅710-7=0
c⋅710-7=0
Move 7 to the left of c.
7c10-7=0
7c10-7=0
7c10-7=0
Add 7 to both sides of the equation.
7c10=7
Multiply both sides of the equation by 107.
107⋅7c10=107⋅7
Simplify both sides of the equation.
Simplify 107⋅7c10.
Cancel the common factor of 10.
Cancel the common factor.
107⋅7c10=107⋅7
Rewrite the expression.
17⋅(7c)=107⋅7
17⋅(7c)=107⋅7
Cancel the common factor of 7.
Factor 7 out of 7c.
17⋅(7(c))=107⋅7
Cancel the common factor.
17⋅(7c)=107⋅7
Rewrite the expression.
c=107⋅7
c=107⋅7
c=107⋅7
Cancel the common factor of 7.
Cancel the common factor.
c=107⋅7
Rewrite the expression.
c=10
c=10
c=10
Solve for c 4/5c-7=1/10c

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