Solve -1x/2+4/5--5/6

$$\frac { - 1 x } { 2 } + \frac { 4 } { 5 } - \frac { - 5 } { 6 }$$

Evaluate

$$-\frac{x}{2}+\frac{49}{30}$$

Short Solution Steps

Fraction \frac{-5}{6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$\frac{-x}{2}+\frac{4}{5}-\left(-\frac{5}{6}\right)$$

The opposite of -\frac{5}{6} is \frac{5}{6}.

$$\frac{-x}{2}+\frac{4}{5}+\frac{5}{6}$$

Least common multiple of 5 and 6 is 30. Convert \frac{4}{5} and \frac{5}{6} to fractions with denominator 30.

$$\frac{-x}{2}+\frac{24}{30}+\frac{25}{30}$$

Since \frac{24}{30} and \frac{25}{30} have the same denominator, add them by adding their numerators.

$$\frac{-x}{2}+\frac{24+25}{30}$$

Add 24 and 25 to get 49.

$$\frac{-x}{2}+\frac{49}{30}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 30 is 30. Multiply \frac{-x}{2} times \frac{15}{15}.

$$\frac{15\left(-1\right)x}{30}+\frac{49}{30}$$

Since \frac{15\left(-1\right)x}{30} and \frac{49}{30} have the same denominator, add them by adding their numerators.

$$\frac{15\left(-1\right)x+49}{30}$$

Do the multiplications in 15\left(-1\right)x+49.

$$\frac{-15x+49}{30}$$

Factor

$$\frac{49-15x}{30}$$

Solution Steps

Factor out \frac{1}{30}.

$$\frac{-15x+49}{30}$$

Consider -15x+24+25. Multiply and combine like terms.

$$-15x+49$$

Rewrite the complete factored expression.

$$\frac{-15x+49}{30}$$