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

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

Solve for x

$$x=6$$

Steps for Solving Linear Equation

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

$$80x+2000-100x=80\left(20-x\right)+100x+160$$

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

$$-20x+2000=80\left(20-x\right)+100x+160$$

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

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

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

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

Add 1600 and 160 to get 1760.

$$-20x+2000=1760+20x$$

Subtract 20x from both sides.

$$-20x+2000-20x=1760$$

Combine -20x and -20x to get -40x.

$$-40x+2000=1760$$

Subtract 2000 from both sides.

$$-40x=1760-2000$$

Subtract 2000 from 1760 to get -240.

$$-40x=-240$$

Divide both sides by -40.

$$x=\frac{-240}{-40}$$

Divide -240 by -40 to get 6.

$$x=6$$