Solve pi*6^2x/(1+10^3x)=282.6

$$\frac { \pi \times 6 ^ { 2 } x } { ( 1 + 10 ^ { 3 } x ) } = 282.6$$

Solve for x

$$x = \frac{157}{20 {(\pi - 7850)}} \approx 0.0010004$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{1}{1000} since division by zero is not defined. Multiply both sides of the equation by 1000x+1.

$$\pi \times 6^{2}x=282.6\left(1000x+1\right)$$

Calculate 6 to the power of 2 and get 36.

$$\pi \times 36x=282.6\left(1000x+1\right)$$

Use the distributive property to multiply 282.6 by 1000x+1.

$$\pi \times 36x=282600x+282.6$$

Subtract 282600x from both sides.

$$\pi \times 36x-282600x=282.6$$

Combine all terms containing x.

$$\left(\pi \times 36-282600\right)x=282.6$$

The equation is in standard form.

$$\left(36\pi -282600\right)x=282.6$$

Divide both sides by 36\pi -282600.

$$\frac{\left(36\pi -282600\right)x}{36\pi -282600}=\frac{282.6}{36\pi -282600}$$

Dividing by 36\pi -282600 undoes the multiplication by 36\pi -282600.

$$x=\frac{282.6}{36\pi -282600}$$

Divide 282.6 by 36\pi -282600.

$$x=\frac{1413}{5\left(36\pi -282600\right)}$$

Variable x cannot be equal to -\frac{1}{1000}.

$$x=\frac{1413}{5\left(36\pi -282600\right)}\text{, }x\neq -\frac{1}{1000}$$