Solve x-3/2-2-x/3>x

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

Solve for x

$$x<-13$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{x-3}{2} times \frac{3}{3}. Multiply \frac{2-x}{3} times \frac{2}{2}.

$$\frac{3\left(x-3\right)}{6}-\frac{2\left(2-x\right)}{6}>x$$

Since \frac{3\left(x-3\right)}{6} and \frac{2\left(2-x\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(x-3\right)-2\left(2-x\right)}{6}>x$$

Do the multiplications in 3\left(x-3\right)-2\left(2-x\right).

$$\frac{3x-9-4+2x}{6}>x$$

Combine like terms in 3x-9-4+2x.

$$\frac{5x-13}{6}>x$$

Divide each term of 5x-13 by 6 to get \frac{5}{6}x-\frac{13}{6}.

$$\frac{5}{6}x-\frac{13}{6}>x$$

Subtract x from both sides.

$$\frac{5}{6}x-\frac{13}{6}-x>0$$

Combine \frac{5}{6}x and -x to get -\frac{1}{6}x.

$$-\frac{1}{6}x-\frac{13}{6}>0$$

Add \frac{13}{6} to both sides. Anything plus zero gives itself.

$$-\frac{1}{6}x>\frac{13}{6}$$

Multiply both sides by -6, the reciprocal of -\frac{1}{6}. Since -\frac{1}{6} is negative, the inequality direction is changed.

$$x<\frac{13}{6}\left(-6\right)$$

Express \frac{13}{6}\left(-6\right) as a single fraction.

$$x<\frac{13\left(-6\right)}{6}$$

Multiply 13 and -6 to get -78.

$$x<\frac{-78}{6}$$

Divide -78 by 6 to get -13.

$$x<-13$$