Solve 4000(20-x)+2500(30+2x)<16000

$$4000(20-x)+2500(30+2x) < 16000$$

Solve for x

$$x<-139$$

Solution Steps

Use the distributive property to multiply 4000 by 20-x.

$$80000-4000x+2500\left(30+2x\right)<16000$$

Use the distributive property to multiply 2500 by 30+2x.

$$80000-4000x+75000+5000x<16000$$

Add 80000 and 75000 to get 155000.

$$155000-4000x+5000x<16000$$

Combine -4000x and 5000x to get 1000x.

$$155000+1000x<16000$$

Subtract 155000 from both sides.

$$1000x<16000-155000$$

Subtract 155000 from 16000 to get -139000.

$$1000x<-139000$$

Divide both sides by 1000. Since 1000 is positive, the inequality direction remains the same.

$$x<\frac{-139000}{1000}$$

Divide -139000 by 1000 to get -139.

$$x<-139$$