Solve sqrt{3}x+sqrt{12}=x+5/sqrt{3}

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

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\sqrt{3}x+2\sqrt{3}=\frac{x+5}{\sqrt{3}}$$

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

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

The square of \sqrt{3} is 3.

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

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

$$\sqrt{3}x+2\sqrt{3}=\frac{x\sqrt{3}+5\sqrt{3}}{3}$$

Subtract \frac{x\sqrt{3}+5\sqrt{3}}{3} from both sides.

$$\sqrt{3}x+2\sqrt{3}-\frac{x\sqrt{3}+5\sqrt{3}}{3}=0$$

Subtract 2\sqrt{3} from both sides. Anything subtracted from zero gives its negation.

$$\sqrt{3}x-\frac{x\sqrt{3}+5\sqrt{3}}{3}=-2\sqrt{3}$$

Multiply both sides of the equation by 3.

$$3\sqrt{3}x-\left(x\sqrt{3}+5\sqrt{3}\right)=-6\sqrt{3}$$

To find the opposite of x\sqrt{3}+5\sqrt{3}, find the opposite of each term.

$$3\sqrt{3}x-x\sqrt{3}-5\sqrt{3}=-6\sqrt{3}$$

Combine 3\sqrt{3}x and -x\sqrt{3} to get 2\sqrt{3}x.

$$2\sqrt{3}x-5\sqrt{3}=-6\sqrt{3}$$

Add 5\sqrt{3} to both sides.

$$2\sqrt{3}x=-6\sqrt{3}+5\sqrt{3}$$

Combine -6\sqrt{3} and 5\sqrt{3} to get -\sqrt{3}.

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

Divide both sides by 2\sqrt{3}.

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

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

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

Divide -\sqrt{3} by 2\sqrt{3}.

$$x=-\frac{1}{2}$$