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\sqrt{3}x-x=100
Subtract x from both sides.
\left(\sqrt{3}-1\right)x=100
Combine all terms containing x.
\frac{\left(\sqrt{3}-1\right)x}{\sqrt{3}-1}=\frac{100}{\sqrt{3}-1}
Divide both sides by \sqrt{3}-1.
x=\frac{100}{\sqrt{3}-1}
Dividing by \sqrt{3}-1 undoes the multiplication by \sqrt{3}-1.
x=50\sqrt{3}+50
Divide 100 by \sqrt{3}-1.