Solve 2-4(16/7-5)-16/7=2(16/7+1)+4

$$2-4( \frac{ 16 }{ 7 } -5)- \frac{ 16 }{ 7 } =2( \frac{ 16 }{ 7 } +1)+4$$

Verify

Solution Steps

Convert 5 to fraction \frac{35}{7}.

$$2-4\left(\frac{16}{7}-\frac{35}{7}\right)-\frac{16}{7}=2\left(\frac{16}{7}+1\right)+4$$

Since \frac{16}{7} and \frac{35}{7} have the same denominator, subtract them by subtracting their numerators.

$$2-4\times \frac{16-35}{7}-\frac{16}{7}=2\left(\frac{16}{7}+1\right)+4$$

Subtract 35 from 16 to get -19.

$$2-4\left(-\frac{19}{7}\right)-\frac{16}{7}=2\left(\frac{16}{7}+1\right)+4$$

Express 4\left(-\frac{19}{7}\right) as a single fraction.

$$2-\frac{4\left(-19\right)}{7}-\frac{16}{7}=2\left(\frac{16}{7}+1\right)+4$$

Multiply 4 and -19 to get -76.

$$2-\frac{-76}{7}-\frac{16}{7}=2\left(\frac{16}{7}+1\right)+4$$

Fraction \frac{-76}{7} can be rewritten as -\frac{76}{7} by extracting the negative sign.

$$2-\left(-\frac{76}{7}\right)-\frac{16}{7}=2\left(\frac{16}{7}+1\right)+4$$

The opposite of -\frac{76}{7} is \frac{76}{7}.

$$2+\frac{76}{7}-\frac{16}{7}=2\left(\frac{16}{7}+1\right)+4$$

Convert 2 to fraction \frac{14}{7}.

$$\frac{14}{7}+\frac{76}{7}-\frac{16}{7}=2\left(\frac{16}{7}+1\right)+4$$

Since \frac{14}{7} and \frac{76}{7} have the same denominator, add them by adding their numerators.

$$\frac{14+76}{7}-\frac{16}{7}=2\left(\frac{16}{7}+1\right)+4$$

Add 14 and 76 to get 90.

$$\frac{90}{7}-\frac{16}{7}=2\left(\frac{16}{7}+1\right)+4$$

Since \frac{90}{7} and \frac{16}{7} have the same denominator, subtract them by subtracting their numerators.

$$\frac{90-16}{7}=2\left(\frac{16}{7}+1\right)+4$$

Subtract 16 from 90 to get 74.

$$\frac{74}{7}=2\left(\frac{16}{7}+1\right)+4$$

Convert 1 to fraction \frac{7}{7}.

$$\frac{74}{7}=2\left(\frac{16}{7}+\frac{7}{7}\right)+4$$

Since \frac{16}{7} and \frac{7}{7} have the same denominator, add them by adding their numerators.

$$\frac{74}{7}=2\times \frac{16+7}{7}+4$$

Add 16 and 7 to get 23.

$$\frac{74}{7}=2\times \frac{23}{7}+4$$

Express 2\times \frac{23}{7} as a single fraction.

$$\frac{74}{7}=\frac{2\times 23}{7}+4$$

Multiply 2 and 23 to get 46.

$$\frac{74}{7}=\frac{46}{7}+4$$

Convert 4 to fraction \frac{28}{7}.

$$\frac{74}{7}=\frac{46}{7}+\frac{28}{7}$$

Since \frac{46}{7} and \frac{28}{7} have the same denominator, add them by adding their numerators.

$$\frac{74}{7}=\frac{46+28}{7}$$

Add 46 and 28 to get 74.

$$\frac{74}{7}=\frac{74}{7}$$

Compare \frac{74}{7} and \frac{74}{7}.

$$\text{true}$$