Solve 2-x/2>2x

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

Solve for x

$$x<\frac{2}{5}$$

Solution Steps

Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.

$$2-x>4x$$

Subtract 4x from both sides.

$$2-x-4x>0$$

Combine -x and -4x to get -5x.

$$2-5x>0$$

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

$$-5x>-2$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

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

Fraction \frac{-2}{-5} can be simplified to \frac{2}{5} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{2}{5}$$