Solve c-0/100-0=m-x/(180-x)-x

$$\frac { c - 0 } { 100 - 0 } = \frac { m - x } { ( 180 - x ) - x }$$

Solve for c

$$c=-\frac{50\left(x-m\right)}{90-x}$$

$$x\neq 90$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(-x+90\right).

$$\left(-\frac{1}{50}x+\frac{9}{5}\right)\left(c-0\right)=m-x$$

Use the distributive property to multiply -\frac{1}{50}x+\frac{9}{5} by c-0.

$$-\frac{1}{50}x\left(c-0\right)+\frac{9}{5}\left(c-0\right)=m-x$$

Reorder the terms.

$$-\frac{1}{50}cx+\frac{9}{5}c=-x+m$$

Combine all terms containing c.

$$\left(-\frac{1}{50}x+\frac{9}{5}\right)c=-x+m$$

The equation is in standard form.

$$\left(-\frac{x}{50}+\frac{9}{5}\right)c=m-x$$

Divide both sides by -\frac{1}{50}x+\frac{9}{5}.

$$\frac{\left(-\frac{x}{50}+\frac{9}{5}\right)c}{-\frac{x}{50}+\frac{9}{5}}=\frac{m-x}{-\frac{x}{50}+\frac{9}{5}}$$

Dividing by -\frac{1}{50}x+\frac{9}{5} undoes the multiplication by -\frac{1}{50}x+\frac{9}{5}.

$$c=\frac{m-x}{-\frac{x}{50}+\frac{9}{5}}$$

Divide m-x by -\frac{1}{50}x+\frac{9}{5}.

$$c=\frac{50\left(m-x\right)}{90-x}$$

Solve for m

$$m=-\frac{cx}{50}+\frac{9c}{5}+x$$

$$x\neq 90$$

Solution Steps

Multiply both sides of the equation by 2\left(-x+90\right).

$$\left(-\frac{1}{50}x+\frac{9}{5}\right)\left(c-0\right)=m-x$$

Use the distributive property to multiply -\frac{1}{50}x+\frac{9}{5} by c-0.

$$-\frac{1}{50}x\left(c-0\right)+\frac{9}{5}\left(c-0\right)=m-x$$

Swap sides so that all variable terms are on the left hand side.

$$m-x=-\frac{1}{50}x\left(c-0\right)+\frac{9}{5}\left(c-0\right)$$

Add x to both sides.

$$m=-\frac{1}{50}x\left(c-0\right)+\frac{9}{5}\left(c-0\right)+x$$

Reorder the terms.

$$m=-\frac{1}{50}cx+x+\frac{9}{5}c$$