Solve 40/1=x/sqrt{3/2}

$$\frac{ 40 }{ 1 } = \frac{ x }{ \frac{ \sqrt{ 3 } }{ 2 } }$$

Solve for x

$$x=20\sqrt{3}\approx 34.641016151$$

Steps for Solving Linear Equation

Anything divided by one gives itself.

$$40=\frac{x}{\frac{\sqrt{3}}{2}}$$

Divide x by \frac{\sqrt{3}}{2} by multiplying x by the reciprocal of \frac{\sqrt{3}}{2}.

$$40=\frac{x\times 2}{\sqrt{3}}$$

Rationalize the denominator of \frac{x\times 2}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$40=\frac{x\times 2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$40=\frac{x\times 2\sqrt{3}}{3}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{x\times 2\sqrt{3}}{3}=40$$

Multiply both sides by 3.

$$x\times 2\sqrt{3}=40\times 3$$

Multiply 40 and 3 to get 120.

$$x\times 2\sqrt{3}=120$$

The equation is in standard form.

$$2\sqrt{3}x=120$$

Divide both sides by 2\sqrt{3}.

$$\frac{2\sqrt{3}x}{2\sqrt{3}}=\frac{120}{2\sqrt{3}}$$

Dividing by 2\sqrt{3} undoes the multiplication by 2\sqrt{3}.

$$x=\frac{120}{2\sqrt{3}}$$

Divide 120 by 2\sqrt{3}.

$$x=20\sqrt{3}$$