Solve 1.11x-5=(x+25)divsqrt{3}

$$1.11x-5=(x+25) \div \sqrt{ 3 }$$

Solve for x

$$x = \frac{327500 \sqrt{3} + 416500}{26963} \approx 36.485058765$$

Steps for Solving Linear Equation

Rationalize the denominator of \frac{x+25}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$1.11x-5=\frac{\left(x+25\right)\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$1.11x-5=\frac{\left(x+25\right)\sqrt{3}}{3}$$

Use the distributive property to multiply x+25 by \sqrt{3}.

$$1.11x-5=\frac{x\sqrt{3}+25\sqrt{3}}{3}$$

Subtract \frac{x\sqrt{3}+25\sqrt{3}}{3} from both sides.

$$1.11x-5-\frac{x\sqrt{3}+25\sqrt{3}}{3}=0$$

Add 5 to both sides. Anything plus zero gives itself.

$$1.11x-\frac{x\sqrt{3}+25\sqrt{3}}{3}=5$$

Multiply both sides of the equation by 3.

$$3.33x-\left(x\sqrt{3}+25\sqrt{3}\right)=15$$

To find the opposite of x\sqrt{3}+25\sqrt{3}, find the opposite of each term.

$$3.33x-x\sqrt{3}-25\sqrt{3}=15$$

Add 25\sqrt{3} to both sides.

$$3.33x-x\sqrt{3}=15+25\sqrt{3}$$

Combine all terms containing x.

$$\left(3.33-\sqrt{3}\right)x=15+25\sqrt{3}$$

The equation is in standard form.

$$\left(3.33-\sqrt{3}\right)x=25\sqrt{3}+15$$

Divide both sides by 3.33-\sqrt{3}.

$$\frac{\left(3.33-\sqrt{3}\right)x}{3.33-\sqrt{3}}=\frac{25\sqrt{3}+15}{3.33-\sqrt{3}}$$

Dividing by 3.33-\sqrt{3} undoes the multiplication by 3.33-\sqrt{3}.

$$x=\frac{25\sqrt{3}+15}{3.33-\sqrt{3}}$$

Divide 15+25\sqrt{3} by 3.33-\sqrt{3}.

$$x=\frac{327500\sqrt{3}+416500}{26963}$$