# Solve for w -6w+1/5=-3/5w-1/3 -6w+15=-35w-13
Simplify each term.
Combine w and 35.
-6w+15=-w⋅35-13
Move 3 to the left of w.
-6w+15=-3w5-13
-6w+15=-3w5-13
Move all terms containing w to the left side of the equation.
Add 3w5 to both sides of the equation.
-6w+15+3w5=-13
To write -6w as a fraction with a common denominator, multiply by 55.
-6w⋅55+3w5+15=-13
Combine -6w and 55.
-6w⋅55+3w5+15=-13
Combine the numerators over the common denominator.
-6w⋅5+3w5+15=-13
Combine the numerators over the common denominator.
-6w⋅5+3w+15=-13
Simplify the numerator.
Multiply 5 by -6.
-30w+3w+15=-13
Add -30w and 3w.
-27w+15=-13
-27w+15=-13
Factor -1 out of -27w.
-(27w)+15=-13
Rewrite 1 as -1(-1).
-(27w)-1(-1)5=-13
Factor -1 out of -(27w)-1(-1).
-(27w-1)5=-13
Rewrite -(27w-1) as -1(27w-1).
-1(27w-1)5=-13
Move the negative in front of the fraction.
-27w-15=-13
-27w-15=-13
Multiply both sides of the equation by -5.
-5⋅(-27w-15)=-5⋅(-13)
Simplify both sides of the equation.
Simplify -5⋅(-27w-15).
Cancel the common factor of 5.
Move the leading negative in -27w-15 into the numerator.
-5⋅-(27w-1)5=-5⋅(-13)
Factor 5 out of -5.
5(-1)⋅-(27w-1)5=-5⋅(-13)
Cancel the common factor.
5⋅-1⋅-(27w-1)5=-5⋅(-13)
Rewrite the expression.
-1⋅(-(27w-1))=-5⋅(-13)
-1⋅(-(27w-1))=-5⋅(-13)
Multiply.
Multiply -1 by -1.
1⋅(27w-1)=-5⋅(-13)
Multiply 27w-1 by 1.
27w-1=-5⋅(-13)
27w-1=-5⋅(-13)
27w-1=-5⋅(-13)
Multiply -5(-13).
Multiply -1 by -5.
27w-1=5(13)
Combine 5 and 13.
27w-1=53
27w-1=53
27w-1=53
Move all terms not containing w to the right side of the equation.
Add 1 to both sides of the equation.
27w=53+1
Write 1 as a fraction with a common denominator.
27w=53+33
Combine the numerators over the common denominator.
27w=5+33
Add 5 and 3.
27w=83
27w=83
Divide each term by 27 and simplify.
Divide each term in 27w=83 by 27.
27w27=83⋅127
Cancel the common factor of 27.
Cancel the common factor.
27w27=83⋅127
Divide w by 1.
w=83⋅127
w=83⋅127
Multiply 83⋅127.
Multiply 83 and 127.
w=83⋅27
Multiply 3 by 27.
w=881
w=881
w=881
The result can be shown in multiple forms.
Exact Form:
w=881
Decimal Form:
w=0.09876543…
Solve for w -6w+1/5=-3/5w-1/3

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