Solve 0.5*640=10*(40-x)*0.75+10*0.2*(40-x)+0.75*10x

$$0.5 \times 640=10 \times (40-x) \times 0.75+10 \times 0.2 \times (40-x)+0.75 \times 10x$$

Solve for x

$$x=30$$

Steps for Solving Linear Equation

Multiply 0.5 and 640 to get 320.

$$320=10\left(40-x\right)\times 0.75+10\times 0.2\left(40-x\right)+0.75\times 10x$$

Multiply 10 and 0.75 to get 7.5.

$$320=7.5\left(40-x\right)+10\times 0.2\left(40-x\right)+0.75\times 10x$$

Use the distributive property to multiply 7.5 by 40-x.

$$320=300-7.5x+10\times 0.2\left(40-x\right)+0.75\times 10x$$

Multiply 10 and 0.2 to get 2.

$$320=300-7.5x+2\left(40-x\right)+0.75\times 10x$$

Use the distributive property to multiply 2 by 40-x.

$$320=300-7.5x+80-2x+0.75\times 10x$$

Add 300 and 80 to get 380.

$$320=380-7.5x-2x+0.75\times 10x$$

Combine -7.5x and -2x to get -9.5x.

$$320=380-9.5x+0.75\times 10x$$

Multiply 0.75 and 10 to get 7.5.

$$320=380-9.5x+7.5x$$

Combine -9.5x and 7.5x to get -2x.

$$320=380-2x$$

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

$$380-2x=320$$

Subtract 380 from both sides.

$$-2x=320-380$$

Subtract 380 from 320 to get -60.

$$-2x=-60$$

Divide both sides by -2.

$$x=\frac{-60}{-2}$$

Divide -60 by -2 to get 30.

$$x=30$$