Solve -x+5/2>x

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

Solve for x

$$x<\frac{5}{3}$$

Solution Steps

Subtract x from both sides.

$$\frac{-x+5}{2}-x>0$$

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

$$-x+5-2x>0$$

Combine -x and -2x to get -3x.

$$-3x+5>0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-3x>-5$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x<\frac{-5}{-3}$$

Fraction \frac{-5}{-3} can be simplified to \frac{5}{3} by removing the negative sign from both the numerator and the denominator.

$$x<\frac{5}{3}$$