Solve 2/3(2x-5)-4/5(4x+7)

$$\frac { 2 } { 3 } ( 2 x - 5 ) - \frac { 4 } { 5 } ( 4 x + 7 )$$

Evaluate

$$\frac{-28x-134}{15}$$

Solution Steps

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

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

Express \frac{2}{3}\times 2 as a single fraction.

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

Multiply 2 and 2 to get 4.

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

Express \frac{2}{3}\left(-5\right) as a single fraction.

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

Multiply 2 and -5 to get -10.

$$\frac{4}{3}x+\frac{-10}{3}-\frac{4}{5}\left(4x+7\right)$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$\frac{4}{3}x-\frac{10}{3}-\frac{4}{5}\left(4x+7\right)$$

Use the distributive property to multiply -\frac{4}{5} by 4x+7.

$$\frac{4}{3}x-\frac{10}{3}-\frac{4}{5}\times 4x-\frac{4}{5}\times 7$$

Express -\frac{4}{5}\times 4 as a single fraction.

$$\frac{4}{3}x-\frac{10}{3}+\frac{-4\times 4}{5}x-\frac{4}{5}\times 7$$

Multiply -4 and 4 to get -16.

$$\frac{4}{3}x-\frac{10}{3}+\frac{-16}{5}x-\frac{4}{5}\times 7$$

Fraction \frac{-16}{5} can be rewritten as -\frac{16}{5} by extracting the negative sign.

$$\frac{4}{3}x-\frac{10}{3}-\frac{16}{5}x-\frac{4}{5}\times 7$$

Express -\frac{4}{5}\times 7 as a single fraction.

$$\frac{4}{3}x-\frac{10}{3}-\frac{16}{5}x+\frac{-4\times 7}{5}$$

Multiply -4 and 7 to get -28.

$$\frac{4}{3}x-\frac{10}{3}-\frac{16}{5}x+\frac{-28}{5}$$

Fraction \frac{-28}{5} can be rewritten as -\frac{28}{5} by extracting the negative sign.

$$\frac{4}{3}x-\frac{10}{3}-\frac{16}{5}x-\frac{28}{5}$$

Combine \frac{4}{3}x and -\frac{16}{5}x to get -\frac{28}{15}x.

$$-\frac{28}{15}x-\frac{10}{3}-\frac{28}{5}$$

Least common multiple of 3 and 5 is 15. Convert -\frac{10}{3} and \frac{28}{5} to fractions with denominator 15.

$$-\frac{28}{15}x-\frac{50}{15}-\frac{84}{15}$$

Since -\frac{50}{15} and \frac{84}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{28}{15}x+\frac{-50-84}{15}$$

Subtract 84 from -50 to get -134.

$$-\frac{28}{15}x-\frac{134}{15}$$

Expand

$$\frac{-28x-134}{15}$$

Solution Steps

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

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

Express \frac{2}{3}\times 2 as a single fraction.

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

Multiply 2 and 2 to get 4.

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

Express \frac{2}{3}\left(-5\right) as a single fraction.

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

Multiply 2 and -5 to get -10.

$$\frac{4}{3}x+\frac{-10}{3}-\frac{4}{5}\left(4x+7\right)$$

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

$$\frac{4}{3}x-\frac{10}{3}-\frac{4}{5}\left(4x+7\right)$$

Use the distributive property to multiply -\frac{4}{5} by 4x+7.

$$\frac{4}{3}x-\frac{10}{3}-\frac{4}{5}\times 4x-\frac{4}{5}\times 7$$

Express -\frac{4}{5}\times 4 as a single fraction.

$$\frac{4}{3}x-\frac{10}{3}+\frac{-4\times 4}{5}x-\frac{4}{5}\times 7$$

Multiply -4 and 4 to get -16.

$$\frac{4}{3}x-\frac{10}{3}+\frac{-16}{5}x-\frac{4}{5}\times 7$$

Fraction \frac{-16}{5} can be rewritten as -\frac{16}{5} by extracting the negative sign.

$$\frac{4}{3}x-\frac{10}{3}-\frac{16}{5}x-\frac{4}{5}\times 7$$

Express -\frac{4}{5}\times 7 as a single fraction.

$$\frac{4}{3}x-\frac{10}{3}-\frac{16}{5}x+\frac{-4\times 7}{5}$$

Multiply -4 and 7 to get -28.

$$\frac{4}{3}x-\frac{10}{3}-\frac{16}{5}x+\frac{-28}{5}$$

Fraction \frac{-28}{5} can be rewritten as -\frac{28}{5} by extracting the negative sign.

$$\frac{4}{3}x-\frac{10}{3}-\frac{16}{5}x-\frac{28}{5}$$

Combine \frac{4}{3}x and -\frac{16}{5}x to get -\frac{28}{15}x.

$$-\frac{28}{15}x-\frac{10}{3}-\frac{28}{5}$$

Least common multiple of 3 and 5 is 15. Convert -\frac{10}{3} and \frac{28}{5} to fractions with denominator 15.

$$-\frac{28}{15}x-\frac{50}{15}-\frac{84}{15}$$

Since -\frac{50}{15} and \frac{84}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{28}{15}x+\frac{-50-84}{15}$$

Subtract 84 from -50 to get -134.

$$-\frac{28}{15}x-\frac{134}{15}$$