Solve 2/5x-5/3+13/2x+2/3-(frac{1}{6}x+frac{1}{4})]=2[(frac{1}{2}-frac{1}{3}x)-frac{5}{4}+frac{13}{12}]

$$\frac { 2 } { 5 } x - \frac { 5 } { 3 } + \frac { 13 } { 2 } x + \frac { 2 } { 3 } - ( \frac { 1 } { 6 } x + \frac { 1 } { 4 } ) ] = 2 [ ( \frac { 1 } { 2 } - \frac { 1 } { 3 } x ) - \frac { 5 } { 4 } + \frac { 13 } { 12 } ]$$

Evaluate

$$\frac{101x}{15}-\frac{5}{4}$$

Solution Steps

Combine \frac{2}{5}x and \frac{13}{2}x to get \frac{69}{10}x.

$$\frac{69}{10}x-\frac{5}{3}+\frac{2}{3}-\left(\frac{1}{6}x+\frac{1}{4}\right)$$

Since -\frac{5}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{69}{10}x+\frac{-5+2}{3}-\left(\frac{1}{6}x+\frac{1}{4}\right)$$

Add -5 and 2 to get -3.

$$\frac{69}{10}x+\frac{-3}{3}-\left(\frac{1}{6}x+\frac{1}{4}\right)$$

Divide -3 by 3 to get -1.

$$\frac{69}{10}x-1-\left(\frac{1}{6}x+\frac{1}{4}\right)$$

To find the opposite of \frac{1}{6}x+\frac{1}{4}, find the opposite of each term.

$$\frac{69}{10}x-1-\frac{1}{6}x-\frac{1}{4}$$

Combine \frac{69}{10}x and -\frac{1}{6}x to get \frac{101}{15}x.

$$\frac{101}{15}x-1-\frac{1}{4}$$

Convert -1 to fraction -\frac{4}{4}.

$$\frac{101}{15}x-\frac{4}{4}-\frac{1}{4}$$

Since -\frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{101}{15}x+\frac{-4-1}{4}$$

Subtract 1 from -4 to get -5.

$$\frac{101}{15}x-\frac{5}{4}$$

Expand

$$\frac{101x}{15}-\frac{5}{4}$$

Solution Steps

Combine \frac{2}{5}x and \frac{13}{2}x to get \frac{69}{10}x.

$$\frac{69}{10}x-\frac{5}{3}+\frac{2}{3}-\left(\frac{1}{6}x+\frac{1}{4}\right)$$

Since -\frac{5}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{69}{10}x+\frac{-5+2}{3}-\left(\frac{1}{6}x+\frac{1}{4}\right)$$

Add -5 and 2 to get -3.

$$\frac{69}{10}x+\frac{-3}{3}-\left(\frac{1}{6}x+\frac{1}{4}\right)$$

Divide -3 by 3 to get -1.

$$\frac{69}{10}x-1-\left(\frac{1}{6}x+\frac{1}{4}\right)$$

To find the opposite of \frac{1}{6}x+\frac{1}{4}, find the opposite of each term.

$$\frac{69}{10}x-1-\frac{1}{6}x-\frac{1}{4}$$

Combine \frac{69}{10}x and -\frac{1}{6}x to get \frac{101}{15}x.

$$\frac{101}{15}x-1-\frac{1}{4}$$

Convert -1 to fraction -\frac{4}{4}.

$$\frac{101}{15}x-\frac{4}{4}-\frac{1}{4}$$

Since -\frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{101}{15}x+\frac{-4-1}{4}$$

Subtract 1 from -4 to get -5.

$$\frac{101}{15}x-\frac{5}{4}$$