Solve 12=x+5/sqrt{3}

$$12 = \frac { x + 5 } { \sqrt { 3 } }$$

Solve for x

$$x=12\sqrt{3}-5\approx 15.784609691$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{x+5}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$12=\frac{\left(x+5\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$12=\frac{\left(x+5\right)\sqrt{3}}{3}$$

Use the distributive property to multiply x+5 by \sqrt{3}.

$$12=\frac{x\sqrt{3}+5\sqrt{3}}{3}$$

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

$$\frac{x\sqrt{3}+5\sqrt{3}}{3}=12$$

Multiply both sides by 3.

$$x\sqrt{3}+5\sqrt{3}=12\times 3$$

Multiply 12 and 3 to get 36.

$$x\sqrt{3}+5\sqrt{3}=36$$

Subtract 5\sqrt{3} from both sides.

$$x\sqrt{3}=36-5\sqrt{3}$$

The equation is in standard form.

$$\sqrt{3}x=36-5\sqrt{3}$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}x}{\sqrt{3}}=\frac{36-5\sqrt{3}}{\sqrt{3}}$$

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

$$x=\frac{36-5\sqrt{3}}{\sqrt{3}}$$

Divide 36-5\sqrt{3} by \sqrt{3}.

$$x=12\sqrt{3}-5$$