Solve (4/9*4-1/3x-2)(-2/5*7)

$$( \frac { 4 } { 9 } \times 4 - \frac { 1 } { 3 } x - 2 ) ( - \frac { 2 } { 5 } \times 7 )$$

Evaluate

$$\frac{14x}{15}+\frac{28}{45}$$

Solution Steps

Express \frac{4}{9}\times 4 as a single fraction.

$$\left(\frac{4\times 4}{9}-\frac{1}{3}x-2\right)\left(-\frac{2}{5}\right)\times 7$$

Multiply 4 and 4 to get 16.

$$\left(\frac{16}{9}-\frac{1}{3}x-2\right)\left(-\frac{2}{5}\right)\times 7$$

Convert 2 to fraction \frac{18}{9}.

$$\left(\frac{16}{9}-\frac{1}{3}x-\frac{18}{9}\right)\left(-\frac{2}{5}\right)\times 7$$

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

$$\left(\frac{16-18}{9}-\frac{1}{3}x\right)\left(-\frac{2}{5}\right)\times 7$$

Subtract 18 from 16 to get -2.

$$\left(-\frac{2}{9}-\frac{1}{3}x\right)\left(-\frac{2}{5}\right)\times 7$$

Express -\frac{2}{5}\times 7 as a single fraction.

$$\left(-\frac{2}{9}-\frac{1}{3}x\right)\times \frac{-2\times 7}{5}$$

Multiply -2 and 7 to get -14.

$$\left(-\frac{2}{9}-\frac{1}{3}x\right)\times \frac{-14}{5}$$

Fraction \frac{-14}{5} can be rewritten as -\frac{14}{5} by extracting the negative sign.

$$\left(-\frac{2}{9}-\frac{1}{3}x\right)\left(-\frac{14}{5}\right)$$

Use the distributive property to multiply -\frac{2}{9}-\frac{1}{3}x by -\frac{14}{5}.

$$-\frac{2}{9}\left(-\frac{14}{5}\right)-\frac{1}{3}x\left(-\frac{14}{5}\right)$$

Multiply -\frac{2}{9} times -\frac{14}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\left(-14\right)}{9\times 5}-\frac{1}{3}x\left(-\frac{14}{5}\right)$$

Do the multiplications in the fraction \frac{-2\left(-14\right)}{9\times 5}.

$$\frac{28}{45}-\frac{1}{3}x\left(-\frac{14}{5}\right)$$

Multiply -\frac{1}{3} times -\frac{14}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{28}{45}+\frac{-\left(-14\right)}{3\times 5}x$$

Do the multiplications in the fraction \frac{-\left(-14\right)}{3\times 5}.

$$\frac{28}{45}+\frac{14}{15}x$$

Expand

$$\frac{14x}{15}+\frac{28}{45}$$

Solution Steps

Express \frac{4}{9}\times 4 as a single fraction.

$$\left(\frac{4\times 4}{9}-\frac{1}{3}x-2\right)\left(-\frac{2}{5}\right)\times 7$$

Multiply 4 and 4 to get 16.

$$\left(\frac{16}{9}-\frac{1}{3}x-2\right)\left(-\frac{2}{5}\right)\times 7$$

Convert 2 to fraction \frac{18}{9}.

$$\left(\frac{16}{9}-\frac{1}{3}x-\frac{18}{9}\right)\left(-\frac{2}{5}\right)\times 7$$

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

$$\left(\frac{16-18}{9}-\frac{1}{3}x\right)\left(-\frac{2}{5}\right)\times 7$$

Subtract 18 from 16 to get -2.

$$\left(-\frac{2}{9}-\frac{1}{3}x\right)\left(-\frac{2}{5}\right)\times 7$$

Express -\frac{2}{5}\times 7 as a single fraction.

$$\left(-\frac{2}{9}-\frac{1}{3}x\right)\times \frac{-2\times 7}{5}$$

Multiply -2 and 7 to get -14.

$$\left(-\frac{2}{9}-\frac{1}{3}x\right)\times \frac{-14}{5}$$

Fraction \frac{-14}{5} can be rewritten as -\frac{14}{5} by extracting the negative sign.

$$\left(-\frac{2}{9}-\frac{1}{3}x\right)\left(-\frac{14}{5}\right)$$

Use the distributive property to multiply -\frac{2}{9}-\frac{1}{3}x by -\frac{14}{5}.

$$-\frac{2}{9}\left(-\frac{14}{5}\right)-\frac{1}{3}x\left(-\frac{14}{5}\right)$$

Multiply -\frac{2}{9} times -\frac{14}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\left(-14\right)}{9\times 5}-\frac{1}{3}x\left(-\frac{14}{5}\right)$$

Do the multiplications in the fraction \frac{-2\left(-14\right)}{9\times 5}.

$$\frac{28}{45}-\frac{1}{3}x\left(-\frac{14}{5}\right)$$

Multiply -\frac{1}{3} times -\frac{14}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{28}{45}+\frac{-\left(-14\right)}{3\times 5}x$$

Do the multiplications in the fraction \frac{-\left(-14\right)}{3\times 5}.

$$\frac{28}{45}+\frac{14}{15}x$$