Solve 1/6w-8/9+2/3w-1/2=

$$\frac { 1 } { 6 } w - \frac { 8 } { 9 } + \frac { 2 } { 3 } w - \frac { 1 } { 2 } =$$

Evaluate

$$\frac{5w}{6}-\frac{25}{18}$$

Solution Steps

Combine \frac{1}{6}w and \frac{2}{3}w to get \frac{5}{6}w.

$$\frac{5}{6}w-\frac{8}{9}-\frac{1}{2}$$

Least common multiple of 9 and 2 is 18. Convert -\frac{8}{9} and \frac{1}{2} to fractions with denominator 18.

$$\frac{5}{6}w-\frac{16}{18}-\frac{9}{18}$$

Since -\frac{16}{18} and \frac{9}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}w+\frac{-16-9}{18}$$

Subtract 9 from -16 to get -25.

$$\frac{5}{6}w-\frac{25}{18}$$

Factor

$$\frac{5\left(3w-5\right)}{18}$$

Solution Steps

Factor out \frac{1}{18}.

$$\frac{15w-25}{18}$$

Consider 3w-16+12w-9. Multiply and combine like terms.

$$15w-25$$

Consider 15w-25. Factor out 5.

$$5\left(3w-5\right)$$

Rewrite the complete factored expression.

$$\frac{5\left(3w-5\right)}{18}$$