Solve 80(20-x)+100x=80x+100(20-x)+160

$$80 ( 20 - x ) + 100 x = 80 x + 100 ( 20 - x ) + 160$$

Solve for x

$$x=14$$

Steps for Solving Linear Equation

Use the distributive property to multiply 80 by 20-x.

$$1600-80x+100x=80x+100\left(20-x\right)+160$$

Combine -80x and 100x to get 20x.

$$1600+20x=80x+100\left(20-x\right)+160$$

Use the distributive property to multiply 100 by 20-x.

$$1600+20x=80x+2000-100x+160$$

Combine 80x and -100x to get -20x.

$$1600+20x=-20x+2000+160$$

Add 2000 and 160 to get 2160.

$$1600+20x=-20x+2160$$

Add 20x to both sides.

$$1600+20x+20x=2160$$

Combine 20x and 20x to get 40x.

$$1600+40x=2160$$

Subtract 1600 from both sides.

$$40x=2160-1600$$

Subtract 1600 from 2160 to get 560.

$$40x=560$$

Divide both sides by 40.

$$x=\frac{560}{40}$$

Divide 560 by 40 to get 14.

$$x=14$$