Solve 4/5(x-2)-1/6(3x-4)=

$$\frac { 4 } { 5 } ( x - 2 ) - \frac { 1 } { 6 } ( 3 x - 4 ) =$$

Evaluate

$$\frac{3x}{10}-\frac{14}{15}$$

Solution Steps

Use the distributive property to multiply \frac{4}{5} by x-2.

$$\frac{4}{5}x+\frac{4}{5}\left(-2\right)-\frac{1}{6}\left(3x-4\right)$$

Express \frac{4}{5}\left(-2\right) as a single fraction.

$$\frac{4}{5}x+\frac{4\left(-2\right)}{5}-\frac{1}{6}\left(3x-4\right)$$

Multiply 4 and -2 to get -8.

$$\frac{4}{5}x+\frac{-8}{5}-\frac{1}{6}\left(3x-4\right)$$

Fraction \frac{-8}{5} can be rewritten as -\frac{8}{5} by extracting the negative sign.

$$\frac{4}{5}x-\frac{8}{5}-\frac{1}{6}\left(3x-4\right)$$

Use the distributive property to multiply -\frac{1}{6} by 3x-4.

$$\frac{4}{5}x-\frac{8}{5}-\frac{1}{6}\times 3x-\frac{1}{6}\left(-4\right)$$

Express -\frac{1}{6}\times 3 as a single fraction.

$$\frac{4}{5}x-\frac{8}{5}+\frac{-3}{6}x-\frac{1}{6}\left(-4\right)$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}x-\frac{8}{5}-\frac{1}{2}x-\frac{1}{6}\left(-4\right)$$

Express -\frac{1}{6}\left(-4\right) as a single fraction.

$$\frac{4}{5}x-\frac{8}{5}-\frac{1}{2}x+\frac{-\left(-4\right)}{6}$$

Multiply -1 and -4 to get 4.

$$\frac{4}{5}x-\frac{8}{5}-\frac{1}{2}x+\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}x-\frac{8}{5}-\frac{1}{2}x+\frac{2}{3}$$

Combine \frac{4}{5}x and -\frac{1}{2}x to get \frac{3}{10}x.

$$\frac{3}{10}x-\frac{8}{5}+\frac{2}{3}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{8}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{3}{10}x-\frac{24}{15}+\frac{10}{15}$$

Since -\frac{24}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{3}{10}x+\frac{-24+10}{15}$$

Add -24 and 10 to get -14.

$$\frac{3}{10}x-\frac{14}{15}$$

Expand

$$\frac{3x}{10}-\frac{14}{15}$$

Solution Steps

Use the distributive property to multiply \frac{4}{5} by x-2.

$$\frac{4}{5}x+\frac{4}{5}\left(-2\right)-\frac{1}{6}\left(3x-4\right)$$

Express \frac{4}{5}\left(-2\right) as a single fraction.

$$\frac{4}{5}x+\frac{4\left(-2\right)}{5}-\frac{1}{6}\left(3x-4\right)$$

Multiply 4 and -2 to get -8.

$$\frac{4}{5}x+\frac{-8}{5}-\frac{1}{6}\left(3x-4\right)$$

Fraction \frac{-8}{5} can be rewritten as -\frac{8}{5} by extracting the negative sign.

$$\frac{4}{5}x-\frac{8}{5}-\frac{1}{6}\left(3x-4\right)$$

Use the distributive property to multiply -\frac{1}{6} by 3x-4.

$$\frac{4}{5}x-\frac{8}{5}-\frac{1}{6}\times 3x-\frac{1}{6}\left(-4\right)$$

Express -\frac{1}{6}\times 3 as a single fraction.

$$\frac{4}{5}x-\frac{8}{5}+\frac{-3}{6}x-\frac{1}{6}\left(-4\right)$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}x-\frac{8}{5}-\frac{1}{2}x-\frac{1}{6}\left(-4\right)$$

Express -\frac{1}{6}\left(-4\right) as a single fraction.

$$\frac{4}{5}x-\frac{8}{5}-\frac{1}{2}x+\frac{-\left(-4\right)}{6}$$

Multiply -1 and -4 to get 4.

$$\frac{4}{5}x-\frac{8}{5}-\frac{1}{2}x+\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}x-\frac{8}{5}-\frac{1}{2}x+\frac{2}{3}$$

Combine \frac{4}{5}x and -\frac{1}{2}x to get \frac{3}{10}x.

$$\frac{3}{10}x-\frac{8}{5}+\frac{2}{3}$$

Least common multiple of 5 and 3 is 15. Convert -\frac{8}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{3}{10}x-\frac{24}{15}+\frac{10}{15}$$

Since -\frac{24}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$\frac{3}{10}x+\frac{-24+10}{15}$$

Add -24 and 10 to get -14.

$$\frac{3}{10}x-\frac{14}{15}$$