Solve [500-(n-50)](x-40)=8000

$$[ 500 - ( n - 50 ) ] ( x - 40 ) = 8000$$

Solve for n

$$n=-\frac{50\left(11x-600\right)}{40-x}$$

$$x\neq 40$$

Steps for Solving Linear Equation

To find the opposite of n-50, find the opposite of each term.

$$\left(500-n+50\right)\left(x-40\right)=8000$$

Add 500 and 50 to get 550.

$$\left(550-n\right)\left(x-40\right)=8000$$

Use the distributive property to multiply 550-n by x-40.

$$550x-22000-nx+40n=8000$$

Subtract 550x from both sides.

$$-22000-nx+40n=8000-550x$$

Add 22000 to both sides.

$$-nx+40n=8000-550x+22000$$

Add 8000 and 22000 to get 30000.

$$-nx+40n=30000-550x$$

Combine all terms containing n.

$$\left(-x+40\right)n=30000-550x$$

The equation is in standard form.

$$\left(40-x\right)n=30000-550x$$

Divide both sides by -x+40.

$$\frac{\left(40-x\right)n}{40-x}=\frac{30000-550x}{40-x}$$

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

$$n=\frac{30000-550x}{40-x}$$

Divide 30000-550x by -x+40.

$$n=\frac{50\left(600-11x\right)}{40-x}$$

Solve for x

$$x=-\frac{40\left(n-750\right)}{550-n}$$

$$n\neq 550$$

Steps for Solving Linear Equation

To find the opposite of n-50, find the opposite of each term.

$$\left(500-n+50\right)\left(x-40\right)=8000$$

Add 500 and 50 to get 550.

$$\left(550-n\right)\left(x-40\right)=8000$$

Use the distributive property to multiply 550-n by x-40.

$$550x-22000-nx+40n=8000$$

Add 22000 to both sides.

$$550x-nx+40n=8000+22000$$

Add 8000 and 22000 to get 30000.

$$550x-nx+40n=30000$$

Subtract 40n from both sides.

$$550x-nx=30000-40n$$

Combine all terms containing x.

$$\left(550-n\right)x=30000-40n$$

Divide both sides by 550-n.

$$\frac{\left(550-n\right)x}{550-n}=\frac{30000-40n}{550-n}$$

Dividing by 550-n undoes the multiplication by 550-n.

$$x=\frac{30000-40n}{550-n}$$

Divide 30000-40n by 550-n.

$$x=\frac{40\left(750-n\right)}{550-n}$$