Solve 400x-10(x-8)+500x-15(x-8)=10500

$$400x-10(x-8)+500x-15(x-8)=10500$$

Solve for x

$$x = \frac{412}{35} = 11\frac{27}{35} \approx 11.771428571$$

Steps for Solving Linear Equation

Use the distributive property to multiply -10 by x-8.

$$400x-10x+80+500x-15\left(x-8\right)=10500$$

Combine 400x and -10x to get 390x.

$$390x+80+500x-15\left(x-8\right)=10500$$

Combine 390x and 500x to get 890x.

$$890x+80-15\left(x-8\right)=10500$$

Use the distributive property to multiply -15 by x-8.

$$890x+80-15x+120=10500$$

Combine 890x and -15x to get 875x.

$$875x+80+120=10500$$

Add 80 and 120 to get 200.

$$875x+200=10500$$

Subtract 200 from both sides.

$$875x=10500-200$$

Subtract 200 from 10500 to get 10300.

$$875x=10300$$

Divide both sides by 875.

$$x=\frac{10300}{875}$$

Reduce the fraction \frac{10300}{875} to lowest terms by extracting and canceling out 25.

$$x=\frac{412}{35}$$