Solve for b
b=\frac{4032061x}{202711967325}+\frac{1626557600167}{162169573860}
Solve for x
x=\frac{202711967325b}{4032061}-\frac{8132788000835}{16128244}
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8108478693\left(200b-x\right)+8100398495\left(2008-x\right)=8092334385\left(2010-x\right)+8084286315\left(2012-x\right)
Multiply both sides of the equation by 16257499779465, the least common multiple of 2005,2007,2009,2011.
1621695738600b-8108478693x+8100398495\left(2008-x\right)=8092334385\left(2010-x\right)+8084286315\left(2012-x\right)
Use the distributive property to multiply 8108478693 by 200b-x.
1621695738600b-8108478693x+16265600177960-8100398495x=8092334385\left(2010-x\right)+8084286315\left(2012-x\right)
Use the distributive property to multiply 8100398495 by 2008-x.
1621695738600b-16208877188x+16265600177960=8092334385\left(2010-x\right)+8084286315\left(2012-x\right)
Combine -8108478693x and -8100398495x to get -16208877188x.
1621695738600b-16208877188x+16265600177960=16265592113850-8092334385x+8084286315\left(2012-x\right)
Use the distributive property to multiply 8092334385 by 2010-x.
1621695738600b-16208877188x+16265600177960=16265592113850-8092334385x+16265584065780-8084286315x
Use the distributive property to multiply 8084286315 by 2012-x.
1621695738600b-16208877188x+16265600177960=32531176179630-8092334385x-8084286315x
Add 16265592113850 and 16265584065780 to get 32531176179630.
1621695738600b-16208877188x+16265600177960=32531176179630-16176620700x
Combine -8092334385x and -8084286315x to get -16176620700x.
1621695738600b+16265600177960=32531176179630-16176620700x+16208877188x
Add 16208877188x to both sides.
1621695738600b+16265600177960=32531176179630+32256488x
Combine -16176620700x and 16208877188x to get 32256488x.
1621695738600b=32531176179630+32256488x-16265600177960
Subtract 16265600177960 from both sides.
1621695738600b=16265576001670+32256488x
Subtract 16265600177960 from 32531176179630 to get 16265576001670.
1621695738600b=32256488x+16265576001670
The equation is in standard form.
\frac{1621695738600b}{1621695738600}=\frac{32256488x+16265576001670}{1621695738600}
Divide both sides by 1621695738600.
b=\frac{32256488x+16265576001670}{1621695738600}
Dividing by 1621695738600 undoes the multiplication by 1621695738600.
b=\frac{4032061x}{202711967325}+\frac{1626557600167}{162169573860}
Divide 16265576001670+32256488x by 1621695738600.
8108478693\left(200b-x\right)+8100398495\left(2008-x\right)=8092334385\left(2010-x\right)+8084286315\left(2012-x\right)
Multiply both sides of the equation by 16257499779465, the least common multiple of 2005,2007,2009,2011.
1621695738600b-8108478693x+8100398495\left(2008-x\right)=8092334385\left(2010-x\right)+8084286315\left(2012-x\right)
Use the distributive property to multiply 8108478693 by 200b-x.
1621695738600b-8108478693x+16265600177960-8100398495x=8092334385\left(2010-x\right)+8084286315\left(2012-x\right)
Use the distributive property to multiply 8100398495 by 2008-x.
1621695738600b-16208877188x+16265600177960=8092334385\left(2010-x\right)+8084286315\left(2012-x\right)
Combine -8108478693x and -8100398495x to get -16208877188x.
1621695738600b-16208877188x+16265600177960=16265592113850-8092334385x+8084286315\left(2012-x\right)
Use the distributive property to multiply 8092334385 by 2010-x.
1621695738600b-16208877188x+16265600177960=16265592113850-8092334385x+16265584065780-8084286315x
Use the distributive property to multiply 8084286315 by 2012-x.
1621695738600b-16208877188x+16265600177960=32531176179630-8092334385x-8084286315x
Add 16265592113850 and 16265584065780 to get 32531176179630.
1621695738600b-16208877188x+16265600177960=32531176179630-16176620700x
Combine -8092334385x and -8084286315x to get -16176620700x.
1621695738600b-16208877188x+16265600177960+16176620700x=32531176179630
Add 16176620700x to both sides.
1621695738600b-32256488x+16265600177960=32531176179630
Combine -16208877188x and 16176620700x to get -32256488x.
-32256488x+16265600177960=32531176179630-1621695738600b
Subtract 1621695738600b from both sides.
-32256488x=32531176179630-1621695738600b-16265600177960
Subtract 16265600177960 from both sides.
-32256488x=16265576001670-1621695738600b
Subtract 16265600177960 from 32531176179630 to get 16265576001670.
\frac{-32256488x}{-32256488}=\frac{16265576001670-1621695738600b}{-32256488}
Divide both sides by -32256488.
x=\frac{16265576001670-1621695738600b}{-32256488}
Dividing by -32256488 undoes the multiplication by -32256488.
x=\frac{202711967325b}{4032061}-\frac{8132788000835}{16128244}
Divide 16265576001670-1621695738600b by -32256488.
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