Solve 1/3(x/7-4)-(x-8/9)

$$\frac { 1 } { 3 } ( \frac { x } { 7 } - 4 ) - ( x - \frac { 8 } { 9 } )$$

Evaluate

$$-\frac{20x}{21}-\frac{4}{9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{7}{7}.

$$\frac{1}{3}\left(\frac{x}{7}-\frac{4\times 7}{7}\right)-\left(x-\frac{8}{9}\right)$$

Since \frac{x}{7} and \frac{4\times 7}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\times \frac{x-4\times 7}{7}-\left(x-\frac{8}{9}\right)$$

Do the multiplications in x-4\times 7.

$$\frac{1}{3}\times \frac{x-28}{7}-\left(x-\frac{8}{9}\right)$$

Multiply \frac{1}{3} times \frac{x-28}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x-28}{3\times 7}-\left(x-\frac{8}{9}\right)$$

Multiply 3 and 7 to get 21.

$$\frac{x-28}{21}-\left(x-\frac{8}{9}\right)$$

To find the opposite of x-\frac{8}{9}, find the opposite of each term.

$$\frac{x-28}{21}-x-\left(-\frac{8}{9}\right)$$

The opposite of -\frac{8}{9} is \frac{8}{9}.

$$\frac{x-28}{21}-x+\frac{8}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 21 and 9 is 63. Multiply \frac{x-28}{21} times \frac{3}{3}. Multiply \frac{8}{9} times \frac{7}{7}.

$$\frac{3\left(x-28\right)}{63}-x+\frac{8\times 7}{63}$$

Since \frac{3\left(x-28\right)}{63} and \frac{8\times 7}{63} have the same denominator, add them by adding their numerators.

$$\frac{3\left(x-28\right)+8\times 7}{63}-x$$

Do the multiplications in 3\left(x-28\right)+8\times 7.

$$\frac{3x-84+56}{63}-x$$

Combine like terms in 3x-84+56.

$$\frac{3x-28}{63}-x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{63}{63}.

$$\frac{3x-28}{63}-\frac{63x}{63}$$

Since \frac{3x-28}{63} and \frac{63x}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x-28-63x}{63}$$

Combine like terms in 3x-28-63x.

$$\frac{-60x-28}{63}$$

Expand

$$-\frac{20x}{21}-\frac{4}{9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{7}{7}.

$$\frac{1}{3}\left(\frac{x}{7}-\frac{4\times 7}{7}\right)-\left(x-\frac{8}{9}\right)$$

Since \frac{x}{7} and \frac{4\times 7}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{3}\times \frac{x-4\times 7}{7}-\left(x-\frac{8}{9}\right)$$

Do the multiplications in x-4\times 7.

$$\frac{1}{3}\times \frac{x-28}{7}-\left(x-\frac{8}{9}\right)$$

Multiply \frac{1}{3} times \frac{x-28}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x-28}{3\times 7}-\left(x-\frac{8}{9}\right)$$

Multiply 3 and 7 to get 21.

$$\frac{x-28}{21}-\left(x-\frac{8}{9}\right)$$

To find the opposite of x-\frac{8}{9}, find the opposite of each term.

$$\frac{x-28}{21}-x-\left(-\frac{8}{9}\right)$$

The opposite of -\frac{8}{9} is \frac{8}{9}.

$$\frac{x-28}{21}-x+\frac{8}{9}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 21 and 9 is 63. Multiply \frac{x-28}{21} times \frac{3}{3}. Multiply \frac{8}{9} times \frac{7}{7}.

$$\frac{3\left(x-28\right)}{63}-x+\frac{8\times 7}{63}$$

Since \frac{3\left(x-28\right)}{63} and \frac{8\times 7}{63} have the same denominator, add them by adding their numerators.

$$\frac{3\left(x-28\right)+8\times 7}{63}-x$$

Do the multiplications in 3\left(x-28\right)+8\times 7.

$$\frac{3x-84+56}{63}-x$$

Combine like terms in 3x-84+56.

$$\frac{3x-28}{63}-x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{63}{63}.

$$\frac{3x-28}{63}-\frac{63x}{63}$$

Since \frac{3x-28}{63} and \frac{63x}{63} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3x-28-63x}{63}$$

Combine like terms in 3x-28-63x.

$$\frac{-60x-28}{63}$$