Solve 3(x-1/2-2x-3/3

$$3 ( \frac { x - 1 } { 2 } - \frac { 2 x - 3 } { 3 }$$

Evaluate

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

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-1}{2} times \frac{3}{3}. Multiply \frac{2x-3}{3} times \frac{2}{2}.

$$3\left(\frac{3\left(x-1\right)}{6}-\frac{2\left(2x-3\right)}{6}\right)$$

Since \frac{3\left(x-1\right)}{6} and \frac{2\left(2x-3\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$3\times \frac{3\left(x-1\right)-2\left(2x-3\right)}{6}$$

Do the multiplications in 3\left(x-1\right)-2\left(2x-3\right).

$$3\times \frac{3x-3-4x+6}{6}$$

Combine like terms in 3x-3-4x+6.

$$3\times \frac{-x+3}{6}$$

Cancel out 6, the greatest common factor in 3 and 6.

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

Expand

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

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-1}{2} times \frac{3}{3}. Multiply \frac{2x-3}{3} times \frac{2}{2}.

$$3\left(\frac{3\left(x-1\right)}{6}-\frac{2\left(2x-3\right)}{6}\right)$$

Since \frac{3\left(x-1\right)}{6} and \frac{2\left(2x-3\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$3\times \frac{3\left(x-1\right)-2\left(2x-3\right)}{6}$$

Do the multiplications in 3\left(x-1\right)-2\left(2x-3\right).

$$3\times \frac{3x-3-4x+6}{6}$$

Combine like terms in 3x-3-4x+6.

$$3\times \frac{-x+3}{6}$$

Cancel out 6, the greatest common factor in 3 and 6.

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