Solve 2x+13=kx

$$2 x + 13 = k x$$

Solve for k

$$k=2+\frac{13}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$kx=2x+13$$

The equation is in standard form.

$$xk=2x+13$$

Divide both sides by x.

$$\frac{xk}{x}=\frac{2x+13}{x}$$

Dividing by x undoes the multiplication by x.

$$k=\frac{2x+13}{x}$$

Divide 2x+13 by x.

$$k=2+\frac{13}{x}$$

Solve for x

$$x=-\frac{13}{2-k}$$

$$k\neq 2$$

Steps for Solving Linear Equation

Subtract kx from both sides.

$$2x+13-kx=0$$

Subtract 13 from both sides. Anything subtracted from zero gives its negation.

$$2x-kx=-13$$

Combine all terms containing x.

$$\left(2-k\right)x=-13$$

Divide both sides by 2-k.

$$\frac{\left(2-k\right)x}{2-k}=-\frac{13}{2-k}$$

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

$$x=-\frac{13}{2-k}$$