Solve 2/3(6x^2-7x/2+13/4)

$$\frac { 2 } { 3 } ( 6 x ^ { 2 } - \frac { 7 x } { 2 } + 1 \frac { 3 } { 4 } )$$

Evaluate

$$4x^{2}-\frac{7x}{3}+\frac{7}{6}$$

Short Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{2}{3}\left(6x^{2}-\frac{7x}{2}+\frac{4+3}{4}\right)$$

Add 4 and 3 to get 7.

$$\frac{2}{3}\left(6x^{2}-\frac{7x}{2}+\frac{7}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{7x}{2} times \frac{2}{2}.

$$\frac{2}{3}\left(6x^{2}-\frac{2\times 7x}{4}+\frac{7}{4}\right)$$

Since -\frac{2\times 7x}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}\left(6x^{2}+\frac{-2\times 7x+7}{4}\right)$$

Do the multiplications in -2\times 7x+7.

$$\frac{2}{3}\left(6x^{2}+\frac{-14x+7}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x^{2} times \frac{4}{4}.

$$\frac{2}{3}\left(\frac{4\times 6x^{2}}{4}+\frac{-14x+7}{4}\right)$$

Since \frac{4\times 6x^{2}}{4} and \frac{-14x+7}{4} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}\times \frac{4\times 6x^{2}-14x+7}{4}$$

Do the multiplications in 4\times 6x^{2}-14x+7.

$$\frac{2}{3}\times \frac{24x^{2}-14x+7}{4}$$

Multiply \frac{2}{3} times \frac{24x^{2}-14x+7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(24x^{2}-14x+7\right)}{3\times 4}$$

Cancel out 2 in both numerator and denominator.

$$\frac{24x^{2}-14x+7}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{24x^{2}-14x+7}{6}$$

Expand

$$4x^{2}-\frac{7x}{3}+\frac{7}{6}$$

Short Solution Steps

Multiply 1 and 4 to get 4.

$$\frac{2}{3}\left(6x^{2}-\frac{7x}{2}+\frac{4+3}{4}\right)$$

Add 4 and 3 to get 7.

$$\frac{2}{3}\left(6x^{2}-\frac{7x}{2}+\frac{7}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{7x}{2} times \frac{2}{2}.

$$\frac{2}{3}\left(6x^{2}-\frac{2\times 7x}{4}+\frac{7}{4}\right)$$

Since -\frac{2\times 7x}{4} and \frac{7}{4} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}\left(6x^{2}+\frac{-2\times 7x+7}{4}\right)$$

Do the multiplications in -2\times 7x+7.

$$\frac{2}{3}\left(6x^{2}+\frac{-14x+7}{4}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x^{2} times \frac{4}{4}.

$$\frac{2}{3}\left(\frac{4\times 6x^{2}}{4}+\frac{-14x+7}{4}\right)$$

Since \frac{4\times 6x^{2}}{4} and \frac{-14x+7}{4} have the same denominator, add them by adding their numerators.

$$\frac{2}{3}\times \frac{4\times 6x^{2}-14x+7}{4}$$

Do the multiplications in 4\times 6x^{2}-14x+7.

$$\frac{2}{3}\times \frac{24x^{2}-14x+7}{4}$$

Multiply \frac{2}{3} times \frac{24x^{2}-14x+7}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(24x^{2}-14x+7\right)}{3\times 4}$$

Cancel out 2 in both numerator and denominator.

$$\frac{24x^{2}-14x+7}{2\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{24x^{2}-14x+7}{6}$$