Solve 2400x+22500=2900(x+6k)

$$2400 x + 22500 = 2900 ( x + 6 k )$$

Solve for k

$$k=-\frac{5x}{174}+\frac{75}{58}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2900 by x+6k.

$$2400x+22500=2900x+17400k$$

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

$$2900x+17400k=2400x+22500$$

Subtract 2900x from both sides.

$$17400k=2400x+22500-2900x$$

Combine 2400x and -2900x to get -500x.

$$17400k=-500x+22500$$

The equation is in standard form.

$$17400k=22500-500x$$

Divide both sides by 17400.

$$\frac{17400k}{17400}=\frac{22500-500x}{17400}$$

Dividing by 17400 undoes the multiplication by 17400.

$$k=\frac{22500-500x}{17400}$$

Divide -500x+22500 by 17400.

$$k=-\frac{5x}{174}+\frac{75}{58}$$

Solve for x

$$x=-\frac{174k}{5}+45$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2900 by x+6k.

$$2400x+22500=2900x+17400k$$

Subtract 2900x from both sides.

$$2400x+22500-2900x=17400k$$

Combine 2400x and -2900x to get -500x.

$$-500x+22500=17400k$$

Subtract 22500 from both sides.

$$-500x=17400k-22500$$

Divide both sides by -500.

$$\frac{-500x}{-500}=\frac{17400k-22500}{-500}$$

Dividing by -500 undoes the multiplication by -500.

$$x=\frac{17400k-22500}{-500}$$

Divide 17400k-22500 by -500.

$$x=-\frac{174k}{5}+45$$