Solve -2x/3+x/2-1/6

$$- \frac{ 2x }{ 3 } + \frac{ x }{ 2 } - \frac{ 1 }{ 6 }$$

Evaluate

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

Short Solution Steps

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

$$-\frac{2\times 2x}{6}+\frac{3x}{6}-\frac{1}{6}$$

Since -\frac{2\times 2x}{6} and \frac{3x}{6} have the same denominator, add them by adding their numerators.

$$\frac{-2\times 2x+3x}{6}-\frac{1}{6}$$

Do the multiplications in -2\times 2x+3x.

$$\frac{-4x+3x}{6}-\frac{1}{6}$$

Combine like terms in -4x+3x.

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

Since \frac{-x}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

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

Factor

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

Solution Steps

Factor out \frac{1}{6}.

$$\frac{-4x+3x-1}{6}$$

Consider -4x+3x-1. Multiply and combine like terms.

$$-x-1$$

Rewrite the complete factored expression.

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