Solve frac{5sqrt{3}x+sqrt{3}}{3}+14=4sqrt{3}x+sqrt{3}

$$\frac{ 5 \sqrt{ 3 } x+ \sqrt{ 3 } }{ 3 } +14=4 \sqrt{ 3 } x+ \sqrt{ 3 }$$

Solve for x

$$x=2\sqrt{3}-\frac{2}{7}\approx 3.178387329$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$5\sqrt{3}x+\sqrt{3}+42=12\sqrt{3}x+3\sqrt{3}$$

Subtract 12\sqrt{3}x from both sides.

$$5\sqrt{3}x+\sqrt{3}+42-12\sqrt{3}x=3\sqrt{3}$$

Combine 5\sqrt{3}x and -12\sqrt{3}x to get -7\sqrt{3}x.

$$-7\sqrt{3}x+\sqrt{3}+42=3\sqrt{3}$$

Subtract \sqrt{3} from both sides.

$$-7\sqrt{3}x+42=3\sqrt{3}-\sqrt{3}$$

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

$$-7\sqrt{3}x+42=2\sqrt{3}$$

Subtract 42 from both sides.

$$-7\sqrt{3}x=2\sqrt{3}-42$$

The equation is in standard form.

$$\left(-7\sqrt{3}\right)x=2\sqrt{3}-42$$

Divide both sides by -7\sqrt{3}.

$$\frac{\left(-7\sqrt{3}\right)x}{-7\sqrt{3}}=\frac{2\sqrt{3}-42}{-7\sqrt{3}}$$

Dividing by -7\sqrt{3} undoes the multiplication by -7\sqrt{3}.

$$x=\frac{2\sqrt{3}-42}{-7\sqrt{3}}$$

Divide 2\sqrt{3}-42 by -7\sqrt{3}.

$$x=2\sqrt{3}-\frac{2}{7}$$