Solve 100x+120(10-3/2x)<1400

$$100x+120(10- \frac{ 3 }{ 2 } x) < 1400$$

Solve for x

$$x>-\frac{5}{2}$$

Solution Steps

Use the distributive property to multiply 120 by 10-\frac{3}{2}x.

$$100x+1200+120\left(-\frac{3}{2}\right)x<1400$$

Express 120\left(-\frac{3}{2}\right) as a single fraction.

$$100x+1200+\frac{120\left(-3\right)}{2}x<1400$$

Multiply 120 and -3 to get -360.

$$100x+1200+\frac{-360}{2}x<1400$$

Divide -360 by 2 to get -180.

$$100x+1200-180x<1400$$

Combine 100x and -180x to get -80x.

$$-80x+1200<1400$$

Subtract 1200 from both sides.

$$-80x<1400-1200$$

Subtract 1200 from 1400 to get 200.

$$-80x<200$$

Divide both sides by -80. Since -80 is negative, the inequality direction is changed.

$$x>\frac{200}{-80}$$

Reduce the fraction \frac{200}{-80} to lowest terms by extracting and canceling out 40.

$$x>-\frac{5}{2}$$