Solve 5/6-1/3(9-z)=

$$\frac { 5 } { 6 } - \frac { 1 } { 3 } ( 9 - z ) =$$

Evaluate

$$\frac{z}{3}-\frac{13}{6}$$

Solution Steps

Use the distributive property to multiply -\frac{1}{3} by 9-z.

$$\frac{5}{6}-\frac{1}{3}\times 9-\frac{1}{3}\left(-1\right)z$$

Express -\frac{1}{3}\times 9 as a single fraction.

$$\frac{5}{6}+\frac{-9}{3}-\frac{1}{3}\left(-1\right)z$$

Divide -9 by 3 to get -3.

$$\frac{5}{6}-3-\frac{1}{3}\left(-1\right)z$$

Multiply -\frac{1}{3} and -1 to get \frac{1}{3}.

$$\frac{5}{6}-3+\frac{1}{3}z$$

Convert 3 to fraction \frac{18}{6}.

$$\frac{5}{6}-\frac{18}{6}+\frac{1}{3}z$$

Since \frac{5}{6} and \frac{18}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-18}{6}+\frac{1}{3}z$$

Subtract 18 from 5 to get -13.

$$-\frac{13}{6}+\frac{1}{3}z$$

Expand

$$\frac{z}{3}-\frac{13}{6}$$

Solution Steps

Use the distributive property to multiply -\frac{1}{3} by 9-z.

$$\frac{5}{6}-\frac{1}{3}\times 9-\frac{1}{3}\left(-1\right)z$$

Express -\frac{1}{3}\times 9 as a single fraction.

$$\frac{5}{6}+\frac{-9}{3}-\frac{1}{3}\left(-1\right)z$$

Divide -9 by 3 to get -3.

$$\frac{5}{6}-3-\frac{1}{3}\left(-1\right)z$$

Multiply -\frac{1}{3} and -1 to get \frac{1}{3}.

$$\frac{5}{6}-3+\frac{1}{3}z$$

Convert 3 to fraction \frac{18}{6}.

$$\frac{5}{6}-\frac{18}{6}+\frac{1}{3}z$$

Since \frac{5}{6} and \frac{18}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5-18}{6}+\frac{1}{3}z$$

Subtract 18 from 5 to get -13.

$$-\frac{13}{6}+\frac{1}{3}z$$