Solve 1/4(x-1)-1/5(x-3)

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

Evaluate

$$\frac{x+7}{20}$$

Solution Steps

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

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

Multiply \frac{1}{4} and -1 to get -\frac{1}{4}.

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

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

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

Express -\frac{1}{5}\left(-3\right) as a single fraction.

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

Multiply -1 and -3 to get 3.

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

Combine \frac{1}{4}x and -\frac{1}{5}x to get \frac{1}{20}x.

$$\frac{1}{20}x-\frac{1}{4}+\frac{3}{5}$$

Least common multiple of 4 and 5 is 20. Convert -\frac{1}{4} and \frac{3}{5} to fractions with denominator 20.

$$\frac{1}{20}x-\frac{5}{20}+\frac{12}{20}$$

Since -\frac{5}{20} and \frac{12}{20} have the same denominator, add them by adding their numerators.

$$\frac{1}{20}x+\frac{-5+12}{20}$$

Add -5 and 12 to get 7.

$$\frac{1}{20}x+\frac{7}{20}$$

Expand

$$\frac{x+7}{20}$$

Solution Steps

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

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

Multiply \frac{1}{4} and -1 to get -\frac{1}{4}.

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

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

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

Express -\frac{1}{5}\left(-3\right) as a single fraction.

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

Multiply -1 and -3 to get 3.

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

Combine \frac{1}{4}x and -\frac{1}{5}x to get \frac{1}{20}x.

$$\frac{1}{20}x-\frac{1}{4}+\frac{3}{5}$$

Least common multiple of 4 and 5 is 20. Convert -\frac{1}{4} and \frac{3}{5} to fractions with denominator 20.

$$\frac{1}{20}x-\frac{5}{20}+\frac{12}{20}$$

Since -\frac{5}{20} and \frac{12}{20} have the same denominator, add them by adding their numerators.

$$\frac{1}{20}x+\frac{-5+12}{20}$$

Add -5 and 12 to get 7.

$$\frac{1}{20}x+\frac{7}{20}$$