# Solve for w 5/2w-7/2=3w-6/5

52w-72=3w-65
Combine 52 and w.
5w2-72=3w-65
Move all terms containing w to the left side of the equation.
Subtract 3w from both sides of the equation.
5w2-72-3w=-65
To write -3w as a fraction with a common denominator, multiply by 22.
5w2-3w⋅22-72=-65
Combine -3w and 22.
5w2+-3w⋅22-72=-65
Combine the numerators over the common denominator.
5w-3w⋅22-72=-65
Combine the numerators over the common denominator.
5w-3w⋅2-72=-65
Simplify the numerator.
Multiply 2 by -3.
5w-6w-72=-65
Subtract 6w from 5w.
-w-72=-65
-w-72=-65
Factor -1 out of -w.
-(w)-72=-65
Rewrite -7 as -1(7).
-(w)-1(7)2=-65
Factor -1 out of -(w)-1(7).
-(w+7)2=-65
Rewrite -(w+7) as -1(w+7).
-1(w+7)2=-65
Move the negative in front of the fraction.
-w+72=-65
-w+72=-65
Multiply both sides of the equation by -2.
-2⋅(-w+72)=-2⋅(-65)
Simplify both sides of the equation.
Simplify -2⋅(-w+72).
Cancel the common factor of 2.
Move the leading negative in -w+72 into the numerator.
-2⋅-(w+7)2=-2⋅(-65)
Factor 2 out of -2.
2(-1)⋅-(w+7)2=-2⋅(-65)
Cancel the common factor.
2⋅-1⋅-(w+7)2=-2⋅(-65)
Rewrite the expression.
-1⋅(-(w+7))=-2⋅(-65)
-1⋅(-(w+7))=-2⋅(-65)
Multiply.
Multiply -1 by -1.
1⋅(w+7)=-2⋅(-65)
Multiply w+7 by 1.
w+7=-2⋅(-65)
w+7=-2⋅(-65)
w+7=-2⋅(-65)
Multiply -2(-65).
Multiply -1 by -2.
w+7=2(65)
Combine 2 and 65.
w+7=2⋅65
Multiply 2 by 6.
w+7=125
w+7=125
w+7=125
Move all terms not containing w to the right side of the equation.
Subtract 7 from both sides of the equation.
w=125-7
To write -7 as a fraction with a common denominator, multiply by 55.
w=125-7⋅55
Combine -7 and 55.
w=125+-7⋅55
Combine the numerators over the common denominator.
w=12-7⋅55
Simplify the numerator.
Multiply -7 by 5.
w=12-355
Subtract 35 from 12.
w=-235
w=-235
Move the negative in front of the fraction.
w=-235
w=-235
The result can be shown in multiple forms.
Exact Form:
w=-235
Decimal Form:
w=-4.6
Mixed Number Form:
w=-435
Solve for w 5/2w-7/2=3w-6/5

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