Solve 2w/x=200/(x+20)+1/2

$$\frac { 2 w } { x } = \frac { 200 } { ( x + 20 ) } + \frac { 1 } { 2 }$$

Solve for w

$$w=\frac{x\left(x+420\right)}{4\left(x+20\right)}$$

$$x\neq 0\text{ and }x\neq -20$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x\left(x+20\right), the least common multiple of x,x+20,2.

$$\left(2x+40\right)\times 2w=2x\times 200+2x\left(x+20\right)\times \frac{1}{2}$$

Use the distributive property to multiply 2x+40 by 2.

$$\left(4x+80\right)w=2x\times 200+2x\left(x+20\right)\times \frac{1}{2}$$

Use the distributive property to multiply 4x+80 by w.

$$4xw+80w=2x\times 200+2x\left(x+20\right)\times \frac{1}{2}$$

Multiply 2 and 200 to get 400.

$$4xw+80w=400x+2x\left(x+20\right)\times \frac{1}{2}$$

Multiply 2 and \frac{1}{2} to get 1.

$$4xw+80w=400x+x\left(x+20\right)$$

Use the distributive property to multiply x by x+20.

$$4xw+80w=400x+x^{2}+20x$$

Combine 400x and 20x to get 420x.

$$4xw+80w=420x+x^{2}$$

Combine all terms containing w.

$$\left(4x+80\right)w=420x+x^{2}$$

The equation is in standard form.

$$\left(4x+80\right)w=x^{2}+420x$$

Divide both sides by 80+4x.

$$\frac{\left(4x+80\right)w}{4x+80}=\frac{x\left(x+420\right)}{4x+80}$$

Dividing by 80+4x undoes the multiplication by 80+4x.

$$w=\frac{x\left(x+420\right)}{4x+80}$$

Divide x\left(420+x\right) by 80+4x.

$$w=\frac{x\left(x+420\right)}{4\left(x+20\right)}$$

Solve for x

$$\left\{\begin{matrix}\\x=2\left(-\sqrt{w^{2}-190w+11025}+w-105\right)\text{, }&\text{unconditionally}\\x=2\left(\sqrt{w^{2}-190w+11025}+w-105\right)\text{, }&w\neq 0\end{matrix}\right.$$