Solve 1/2x+2<2x

$$\frac { 1 } { 2 } x + 2 < 2 x$$

Solve for x

$$x>\frac{4}{3}$$

Solution Steps

Subtract 2x from both sides.

$$\frac{1}{2}x+2-2x<0$$

Combine \frac{1}{2}x and -2x to get -\frac{3}{2}x.

$$-\frac{3}{2}x+2<0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{3}{2}x<-2$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}. Since -\frac{3}{2} is negative, the inequality direction is changed.

$$x>-2\left(-\frac{2}{3}\right)$$

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

$$x>\frac{-2\left(-2\right)}{3}$$

Multiply -2 and -2 to get 4.

$$x>\frac{4}{3}$$