Solve x(600-500m)+124+40m+500=12000

$$x ( 600 - 500 m ) + 124 + 40 m + 500 = 12000$$

Solve for m

$$m=-\frac{6\left(25x-474\right)}{5\left(2-25x\right)}$$

$$x\neq \frac{2}{25}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 600-500m.

$$600x-500xm+124+40m+500=12000$$

Add 124 and 500 to get 624.

$$600x-500xm+624+40m=12000$$

Subtract 600x from both sides.

$$-500xm+624+40m=12000-600x$$

Subtract 624 from both sides.

$$-500xm+40m=12000-600x-624$$

Subtract 624 from 12000 to get 11376.

$$-500xm+40m=11376-600x$$

Combine all terms containing m.

$$\left(-500x+40\right)m=11376-600x$$

The equation is in standard form.

$$\left(40-500x\right)m=11376-600x$$

Divide both sides by -500x+40.

$$\frac{\left(40-500x\right)m}{40-500x}=\frac{11376-600x}{40-500x}$$

Dividing by -500x+40 undoes the multiplication by -500x+40.

$$m=\frac{11376-600x}{40-500x}$$

Divide 11376-600x by -500x+40.

$$m=\frac{6\left(474-25x\right)}{5\left(2-25x\right)}$$

Solve for x

$$x=-\frac{2\left(5m-1422\right)}{25\left(6-5m\right)}$$

$$m\neq \frac{6}{5}$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by 600-500m.

$$600x-500xm+124+40m+500=12000$$

Add 124 and 500 to get 624.

$$600x-500xm+624+40m=12000$$

Subtract 624 from both sides.

$$600x-500xm+40m=12000-624$$

Subtract 624 from 12000 to get 11376.

$$600x-500xm+40m=11376$$

Subtract 40m from both sides.

$$600x-500xm=11376-40m$$

Combine all terms containing x.

$$\left(600-500m\right)x=11376-40m$$

Divide both sides by 600-500m.

$$\frac{\left(600-500m\right)x}{600-500m}=\frac{11376-40m}{600-500m}$$

Dividing by 600-500m undoes the multiplication by 600-500m.

$$x=\frac{11376-40m}{600-500m}$$

Divide 11376-40m by 600-500m.

$$x=\frac{2\left(1422-5m\right)}{25\left(6-5m\right)}$$