Solve 18=6lambda+lambda(x-13)

$$18 = 6 \lambda + \lambda ( x - 13 )$$

Solve for x

$$x=7+\frac{18}{\lambda }$$

$$\lambda \neq 0$$

Steps for Solving Linear Equation

Use the distributive property to multiply \lambda by x-13.

$$18=6\lambda +\lambda x-13\lambda$$

Combine 6\lambda and -13\lambda to get -7\lambda .

$$18=-7\lambda +\lambda x$$

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

$$-7\lambda +\lambda x=18$$

Add 7\lambda to both sides.

$$\lambda x=18+7\lambda$$

The equation is in standard form.

$$\lambda x=7\lambda +18$$

Divide both sides by \lambda .

$$\frac{\lambda x}{\lambda }=\frac{7\lambda +18}{\lambda }$$

Dividing by \lambda undoes the multiplication by \lambda .

$$x=\frac{7\lambda +18}{\lambda }$$

Divide 18+7\lambda by \lambda .

$$x=7+\frac{18}{\lambda }$$

Solve for λ

$$\lambda =-\frac{18}{7-x}$$

$$x\neq 7$$

Steps for Solving Linear Equation

Use the distributive property to multiply \lambda by x-13.

$$18=6\lambda +\lambda x-13\lambda$$

Combine 6\lambda and -13\lambda to get -7\lambda .

$$18=-7\lambda +\lambda x$$

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

$$-7\lambda +\lambda x=18$$

Combine all terms containing \lambda .

$$\left(-7+x\right)\lambda =18$$

The equation is in standard form.

$$\left(x-7\right)\lambda =18$$

Divide both sides by x-7.

$$\frac{\left(x-7\right)\lambda }{x-7}=\frac{18}{x-7}$$

Dividing by x-7 undoes the multiplication by x-7.

$$\lambda =\frac{18}{x-7}$$