# Solve for c (7c-4)/10+(2c-9)/5+2=(3c-4)/3+1 7c-410+2c-95+2=3c-43+1
Simplify 7c-410+2c-95+2.
Find the common denominator.
Multiply 2c-95 by 22.
7c-410+2c-95⋅22+2=3c-43+1
Combine.
7c-410+(2c-9)⋅25⋅2+2=3c-43+1
Write 2 as a fraction with denominator 1.
7c-410+(2c-9)⋅25⋅2+21=3c-43+1
Multiply 21 by 1010.
7c-410+(2c-9)⋅25⋅2+21⋅1010=3c-43+1
Multiply 21 and 1010.
7c-410+(2c-9)⋅25⋅2+2⋅1010=3c-43+1
Reorder the factors of 5⋅2.
7c-410+(2c-9)⋅22⋅5+2⋅1010=3c-43+1
Multiply 2 by 5.
7c-410+(2c-9)⋅210+2⋅1010=3c-43+1
7c-410+(2c-9)⋅210+2⋅1010=3c-43+1
Multiply 2 by 10.
7c-410+(2c-9)⋅210+2010=3c-43+1
Combine the numerators over the common denominator.
7c-4+(2c-9)⋅2+2010=3c-43+1
Simplify the numerator.
Apply the distributive property.
7c-4+2c⋅2-9⋅2+2010=3c-43+1
Multiply 2 by 2.
7c-4+4c-9⋅2+2010=3c-43+1
Multiply -9 by 2.
7c-4+4c-18+2010=3c-43+1
11c-4-18+2010=3c-43+1
Subtract 18 from -4.
11c-22+2010=3c-43+1
11c-210=3c-43+1
11c-210=3c-43+1
11c-210=3c-43+1
Simplify 3c-43+1.
Write 1 as a fraction with a common denominator.
11c-210=3c-43+33
Combine the numerators over the common denominator.
11c-210=3c-4+33
11c-210=3c-13
11c-210=3c-13
Move all terms containing c to the left side of the equation.
Subtract 3c-13 from both sides of the equation.
11c-210-3c-13=0
To write 11c-210 as a fraction with a common denominator, multiply by 33.
11c-210⋅33-3c-13=0
To write -3c-13 as a fraction with a common denominator, multiply by 1010.
11c-210⋅33-3c-13⋅1010=0
Write each expression with a common denominator of 30, by multiplying each by an appropriate factor of 1.
Multiply 11c-210 and 33.
(11c-2)⋅310⋅3-3c-13⋅1010=0
Multiply 10 by 3.
(11c-2)⋅330-3c-13⋅1010=0
Multiply 3c-13 and 1010.
(11c-2)⋅330-(3c-1)⋅103⋅10=0
Multiply 3 by 10.
(11c-2)⋅330-(3c-1)⋅1030=0
(11c-2)⋅330-(3c-1)⋅1030=0
Combine the numerators over the common denominator.
(11c-2)⋅3-(3c-1)⋅1030=0
Simplify the numerator.
Apply the distributive property.
11c⋅3-2⋅3-(3c-1)⋅1030=0
Multiply 3 by 11.
33c-2⋅3-(3c-1)⋅1030=0
Multiply -2 by 3.
33c-6-(3c-1)⋅1030=0
Apply the distributive property.
33c-6+(-(3c)–1)⋅1030=0
Multiply 3 by -1.
33c-6+(-3c–1)⋅1030=0
Multiply -1 by -1.
33c-6+(-3c+1)⋅1030=0
Apply the distributive property.
33c-6-3c⋅10+1⋅1030=0
Multiply 10 by -3.
33c-6-30c+1⋅1030=0
Multiply 10 by 1.
33c-6-30c+1030=0
Subtract 30c from 33c.
3c-6+1030=0
3c+430=0
3c+430=0
Split the fraction into multiple fractions.
3c30+430=0
Reduce the expression 3c30 by cancelling the common factors.
Factor 3 out of 3c.
3(c)30+430=0
Factor 3 out of 30.
3c3⋅10+430=0
Cancel the common factor.
3c3⋅10+430=0
Rewrite the expression.
c10+430=0
c10+430=0
Reduce the expression 430 by cancelling the common factors.
Factor 2 out of 4.
c10+2(2)30=0
Factor 2 out of 30.
c10+2⋅22⋅15=0
Cancel the common factor.
c10+2⋅22⋅15=0
Rewrite the expression.
c10+215=0
c10+215=0
c10+215=0
Subtract 215 from both sides of the equation.
c10=-215
Multiply both sides of the equation by 10.
10⋅c10=10⋅(-215)
Simplify both sides of the equation.
Cancel the common factor of 10.
Cancel the common factor.
10⋅c10=10⋅(-215)
Rewrite the expression.
c=10⋅(-215)
c=10⋅(-215)
Simplify 10⋅(-215).
Cancel the common factor of 5.
Move the leading negative in -215 into the numerator.
c=10⋅-215
Factor 5 out of 10.
c=5(2)⋅-215
Factor 5 out of 15.
c=5⋅2⋅-25⋅3
Cancel the common factor.
c=5⋅2⋅-25⋅3
Rewrite the expression.
c=2⋅-23
c=2⋅-23
Combine 2 and -23.
c=2⋅-23
Simplify the expression.
Multiply 2 by -2.
c=-43
Move the negative in front of the fraction.
c=-43
c=-43
c=-43
c=-43
The result can be shown in multiple forms.
Exact Form:
c=-43
Decimal Form:
c=-1.3‾
Mixed Number Form:
c=-113
Solve for c (7c-4)/10+(2c-9)/5+2=(3c-4)/3+1

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