Solve for v
v=-3\left(\sqrt{3}-1\right)x
Solve for x
x=\frac{\left(-\sqrt{3}-1\right)v}{6}
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3x-v=3x\sqrt{3}
Multiply both sides of the equation by 3.
-v=3x\sqrt{3}-3x
Subtract 3x from both sides.
-v=3\sqrt{3}x-3x
The equation is in standard form.
\frac{-v}{-1}=\frac{3\left(\sqrt{3}-1\right)x}{-1}
Divide both sides by -1.
v=\frac{3\left(\sqrt{3}-1\right)x}{-1}
Dividing by -1 undoes the multiplication by -1.
v=-3\left(\sqrt{3}-1\right)x
Divide 3x\left(-1+\sqrt{3}\right) by -1.
3x-v=3x\sqrt{3}
Multiply both sides of the equation by 3.
3x-v-3x\sqrt{3}=0
Subtract 3x\sqrt{3} from both sides.
3x-3x\sqrt{3}=v
Add v to both sides. Anything plus zero gives itself.
\left(3-3\sqrt{3}\right)x=v
Combine all terms containing x.
\frac{\left(3-3\sqrt{3}\right)x}{3-3\sqrt{3}}=\frac{v}{3-3\sqrt{3}}
Divide both sides by 3-3\sqrt{3}.
x=\frac{v}{3-3\sqrt{3}}
Dividing by 3-3\sqrt{3} undoes the multiplication by 3-3\sqrt{3}.
x=\frac{-\sqrt{3}v-v}{6}
Divide v by 3-3\sqrt{3}.
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