Solve for w -4/3w+2/7=-3/7w-3/7

Math
-43w+27=-37w-37
Simplify each term.
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Combine w and 43.
-w⋅43+27=-37w-37
Move 4 to the left of w.
-4w3+27=-37w-37
-4w3+27=-37w-37
Simplify each term.
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Combine w and 37.
-4w3+27=-w⋅37-37
Move 3 to the left of w.
-4w3+27=-3w7-37
-4w3+27=-3w7-37
Move all terms containing w to the left side of the equation.
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Add 3w7 to both sides of the equation.
-4w3+27+3w7=-37
To write -4w3 as a fraction with a common denominator, multiply by 77.
-4w3⋅77+3w7+27=-37
To write 3w7 as a fraction with a common denominator, multiply by 33.
-4w3⋅77+3w7⋅33+27=-37
Write each expression with a common denominator of 21, by multiplying each by an appropriate factor of 1.
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Multiply 4w3 and 77.
-4w⋅73⋅7+3w7⋅33+27=-37
Multiply 3 by 7.
-4w⋅721+3w7⋅33+27=-37
Multiply 3w7 and 33.
-4w⋅721+3w⋅37⋅3+27=-37
Multiply 7 by 3.
-4w⋅721+3w⋅321+27=-37
-4w⋅721+3w⋅321+27=-37
Combine the numerators over the common denominator.
-4w⋅7+3w⋅321+27=-37
Simplify each term.
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Simplify the numerator.
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Factor w out of -4w⋅7+3w⋅3.
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Factor w out of -4w⋅7.
w(-4⋅7)+3w⋅321+27=-37
Factor w out of 3w⋅3.
w(-4⋅7)+w(3⋅3)21+27=-37
Factor w out of w(-4⋅7)+w(3⋅3).
w(-4⋅7+3⋅3)21+27=-37
w(-4⋅7+3⋅3)21+27=-37
Multiply -4 by 7.
w(-28+3⋅3)21+27=-37
Multiply 3 by 3.
w(-28+9)21+27=-37
Add -28 and 9.
w⋅-1921+27=-37
w⋅-1921+27=-37
Move -19 to the left of w.
-19⋅w21+27=-37
Move the negative in front of the fraction.
-19w21+27=-37
-19w21+27=-37
-19w21+27=-37
Move all terms not containing w to the right side of the equation.
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Subtract 27 from both sides of the equation.
-19w21=-37-27
Combine the numerators over the common denominator.
-19w21=-3-27
Subtract 2 from -3.
-19w21=-57
Move the negative in front of the fraction.
-19w21=-57
-19w21=-57
Multiply both sides of the equation by -2119.
-2119⋅(-19w21)=-2119⋅(-57)
Simplify both sides of the equation.
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Simplify -2119⋅(-19w21).
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Cancel the common factor of 21.
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Move the leading negative in -2119 into the numerator.
-2119⋅(-19w21)=-2119⋅(-57)
Move the leading negative in -19w21 into the numerator.
-2119⋅-19w21=-2119⋅(-57)
Factor 21 out of -21.
21(-1)19⋅-19w21=-2119⋅(-57)
Cancel the common factor.
21⋅-119⋅-19w21=-2119⋅(-57)
Rewrite the expression.
-119⋅(-19w)=-2119⋅(-57)
-119⋅(-19w)=-2119⋅(-57)
Cancel the common factor of 19.
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Factor 19 out of -19w.
-119⋅(19(-w))=-2119⋅(-57)
Cancel the common factor.
-119⋅(19(-w))=-2119⋅(-57)
Rewrite the expression.
-1⋅(-w)=-2119⋅(-57)
-1⋅(-w)=-2119⋅(-57)
Multiply.
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Multiply -1 by -1.
1⋅w=-2119⋅(-57)
Multiply w by 1.
w=-2119⋅(-57)
w=-2119⋅(-57)
w=-2119⋅(-57)
Simplify -2119⋅(-57).
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Cancel the common factor of 7.
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Move the leading negative in -2119 into the numerator.
w=-2119⋅(-57)
Move the leading negative in -57 into the numerator.
w=-2119⋅-57
Factor 7 out of -21.
w=7(-3)19⋅-57
Cancel the common factor.
w=7⋅-319⋅-57
Rewrite the expression.
w=-319⋅-5
w=-319⋅-5
Combine -319 and -5.
w=-3⋅-519
Multiply -3 by -5.
w=1519
w=1519
w=1519
The result can be shown in multiple forms.
Exact Form:
w=1519
Decimal Form:
w=0.78947368…
Solve for w -4/3w+2/7=-3/7w-3/7

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