Solve 80x+110(10-x)<1000

$$80x+110(10-x) < 1000$$

Solve for x

$$x>\frac{10}{3}$$

Solution Steps

Use the distributive property to multiply 110 by 10-x.

$$80x+1100-110x<1000$$

Combine 80x and -110x to get -30x.

$$-30x+1100<1000$$

Subtract 1100 from both sides.

$$-30x<1000-1100$$

Subtract 1100 from 1000 to get -100.

$$-30x<-100$$

Divide both sides by -30. Since -30 is negative, the inequality direction is changed.

$$x>\frac{-100}{-30}$$

Reduce the fraction \frac{-100}{-30} to lowest terms by extracting and canceling out -10.

$$x>\frac{10}{3}$$