Solve x/3+1-x/2>x/2

$$\frac{ x }{ 3 } + \frac{ 1-x }{ 2 } > \frac{ x }{ 2 }$$

Solve for x

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

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2x+3\left(1-x\right)>3x$$

Use the distributive property to multiply 3 by 1-x.

$$2x+3-3x>3x$$

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

$$-x+3>3x$$

Subtract 3x from both sides.

$$-x+3-3x>0$$

Combine -x and -3x to get -4x.

$$-4x+3>0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-4x>-3$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x<\frac{-3}{-4}$$

Fraction \frac{-3}{-4} can be simplified to \frac{3}{4} by removing the negative sign from both the numerator and the denominator.

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