Solve 3x+4/x-5=2quadc

$$\frac { 3 x + 4 } { x - 5 } = 2 \quad c$$

Solve for c

$$c=-\frac{3x+4}{2\left(5-x\right)}$$

$$x\neq 5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-5.

$$3x+4=2c\left(x-5\right)$$

Use the distributive property to multiply 2c by x-5.

$$3x+4=2cx-10c$$

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

$$2cx-10c=3x+4$$

Combine all terms containing c.

$$\left(2x-10\right)c=3x+4$$

Divide both sides by 2x-10.

$$\frac{\left(2x-10\right)c}{2x-10}=\frac{3x+4}{2x-10}$$

Dividing by 2x-10 undoes the multiplication by 2x-10.

$$c=\frac{3x+4}{2x-10}$$

Divide 3x+4 by 2x-10.

$$c=\frac{3x+4}{2\left(x-5\right)}$$

Solve for x

$$x=-\frac{2\left(5c+2\right)}{3-2c}$$

$$c\neq \frac{3}{2}$$

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.

$$3x+4=2c\left(x-5\right)$$

Use the distributive property to multiply 2c by x-5.

$$3x+4=2cx-10c$$

Subtract 2cx from both sides.

$$3x+4-2cx=-10c$$

Subtract 4 from both sides.

$$3x-2cx=-10c-4$$

Combine all terms containing x.

$$\left(3-2c\right)x=-10c-4$$

Divide both sides by 3-2c.

$$\frac{\left(3-2c\right)x}{3-2c}=\frac{-10c-4}{3-2c}$$

Dividing by 3-2c undoes the multiplication by 3-2c.

$$x=\frac{-10c-4}{3-2c}$$

Divide -4-10c by 3-2c.

$$x=-\frac{2\left(5c+2\right)}{3-2c}$$

Variable x cannot be equal to 5.

$$x=-\frac{2\left(5c+2\right)}{3-2c}\text{, }x\neq 5$$