Solve (k+1)*x-3(x+6)=5k

$$( k + 1 ) \cdot x - 3 ( x + 6 ) = 5 k$$

Solve for k

$$k=\frac{2\left(x+9\right)}{x-5}$$

$$x\neq 5$$

Steps for Solving Linear Equation

Use the distributive property to multiply k+1 by x.

$$kx+x-3\left(x+6\right)=5k$$

Use the distributive property to multiply -3 by x+6.

$$kx+x-3x-18=5k$$

Combine x and -3x to get -2x.

$$kx-2x-18=5k$$

Subtract 5k from both sides.

$$kx-2x-18-5k=0$$

Add 2x to both sides. Anything plus zero gives itself.

$$kx-18-5k=2x$$

Add 18 to both sides.

$$kx-5k=2x+18$$

Combine all terms containing k.

$$\left(x-5\right)k=2x+18$$

Divide both sides by x-5.

$$\frac{\left(x-5\right)k}{x-5}=\frac{2x+18}{x-5}$$

Dividing by x-5 undoes the multiplication by x-5.

$$k=\frac{2x+18}{x-5}$$

Divide 18+2x by x-5.

$$k=\frac{2\left(x+9\right)}{x-5}$$

Solve for x

$$x=\frac{5k+18}{k-2}$$

$$k\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply k+1 by x.

$$kx+x-3\left(x+6\right)=5k$$

Use the distributive property to multiply -3 by x+6.

$$kx+x-3x-18=5k$$

Combine x and -3x to get -2x.

$$kx-2x-18=5k$$

Add 18 to both sides.

$$kx-2x=5k+18$$

Combine all terms containing x.

$$\left(k-2\right)x=5k+18$$

Divide both sides by k-2.

$$\frac{\left(k-2\right)x}{k-2}=\frac{5k+18}{k-2}$$

Dividing by k-2 undoes the multiplication by k-2.

$$x=\frac{5k+18}{k-2}$$