Solve 4000(22-x)+2500(26+2x)<16000

$$4000(22-x)+2500(26+2x) < 16000$$

Solve for x

$$x<-137$$

Solution Steps

Use the distributive property to multiply 4000 by 22-x.

$$88000-4000x+2500\left(26+2x\right)<16000$$

Use the distributive property to multiply 2500 by 26+2x.

$$88000-4000x+65000+5000x<16000$$

Add 88000 and 65000 to get 153000.

$$153000-4000x+5000x<16000$$

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

$$153000+1000x<16000$$

Subtract 153000 from both sides.

$$1000x<16000-153000$$

Subtract 153000 from 16000 to get -137000.

$$1000x<-137000$$

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

$$x<\frac{-137000}{1000}$$

Divide -137000 by 1000 to get -137.

$$x<-137$$