Solve for x
x = \frac{200}{3} = 66\frac{2}{3} \approx 66.666666667
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\left(x-100\right)\times 180=-x\times 90
Variable x cannot be equal to any of the values 0,100 since division by zero is not defined. Multiply both sides of the equation by x\left(x-100\right), the least common multiple of x,100-x.
180x-18000=-x\times 90
Use the distributive property to multiply x-100 by 180.
180x-18000=-90x
Multiply -1 and 90 to get -90.
180x-18000+90x=0
Add 90x to both sides.
270x-18000=0
Combine 180x and 90x to get 270x.
270x=18000
Add 18000 to both sides. Anything plus zero gives itself.
x=\frac{18000}{270}
Divide both sides by 270.
x=\frac{200}{3}
Reduce the fraction \frac{18000}{270} to lowest terms by extracting and canceling out 90.
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