Solve x-2/5-x=m/x-5

$$\frac{ x-2 }{ 5-x } = \frac{ m }{ x-5 }$$

Solve for m

$$m=2-x$$

$$x\neq 5$$

Solution Steps

Multiply both sides of the equation by x-5, the least common multiple of 5-x,x-5.

$$-\left(x-2\right)=m$$

To find the opposite of x-2, find the opposite of each term.

$$-x+2=m$$

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

$$m=-x+2$$

Solve for x

$$x=2-m$$

$$m\neq -3$$

Steps for Solving Linear Equation

Variable x cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by x-5, the least common multiple of 5-x,x-5.

$$-\left(x-2\right)=m$$

To find the opposite of x-2, find the opposite of each term.

$$-x+2=m$$

Subtract 2 from both sides.

$$-x=m-2$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{m-2}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{m-2}{-1}$$

Divide m-2 by -1.

$$x=2-m$$

Variable x cannot be equal to 5.

$$x=2-m\text{, }x\neq 5$$