1) Risolvere la seguente equazione: $$ \frac{x \sqrt{3}-1}{\sqrt{3}}=\sqrt{3}-x $$

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Solve the equation $$ \frac{x \sqrt{3}-1}{\sqrt{3}}=\sqrt{3}-x $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{x\sqrt{3}-1}{\sqrt{3}}=\sqrt{3}-x$$
- step1: Calculate:
  $$\frac{\sqrt{3}	imes x-1}{\sqrt{3}}=\sqrt{3}-x$$
- step2: Multiply both sides of the equation by LCD:
  $$\frac{\sqrt{3}	imes x-1}{\sqrt{3}}	imes \sqrt{3}=\left(\sqrt{3}-xight)\sqrt{3}$$
- step3: Simplify the equation:
  $$\sqrt{3}	imes x-1=3-\sqrt{3}	imes x$$
- step4: Move the expression to the left side:
  $$\sqrt{3}	imes x+\sqrt{3}	imes x=3+1$$
- step5: Add and subtract:
  $$2\sqrt{3}	imes x=3+1$$
- step6: Add and subtract:
  $$2\sqrt{3}	imes x=4$$
- step7: Divide both sides:
  $$\frac{2\sqrt{3}	imes x}{2\sqrt{3}}=\frac{4}{2\sqrt{3}}$$
- step8: Divide the numbers:
  $$x=\frac{2}{\sqrt{3}}$$
- step9: Rearrange the numbers:
  $$x=\frac{2\sqrt{3}}{3}$$
La soluzione dell'equazione $$ \frac{x \sqrt{3}-1}{\sqrt{3}}=\sqrt{3}-x $$ è $$ x = \frac{2\sqrt{3}}{3} $$.
$$ x = \frac{2\sqrt{3}}{3} $$

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