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

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

Evaluate

$$\frac{x+5}{6}$$

Solution Steps

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

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

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

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

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

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

Use the distributive property to multiply -\frac{1}{3} by 7x-4.

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

Express -\frac{1}{3}\times 7 as a single fraction.

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

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

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

Express -\frac{1}{3}\left(-4\right) as a single fraction.

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

Multiply -1 and -4 to get 4.

$$\frac{5}{2}x-\frac{1}{2}-\frac{7}{3}x+\frac{4}{3}$$

Combine \frac{5}{2}x and -\frac{7}{3}x to get \frac{1}{6}x.

$$\frac{1}{6}x-\frac{1}{2}+\frac{4}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{1}{6}x-\frac{3}{6}+\frac{8}{6}$$

Since -\frac{3}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}x+\frac{-3+8}{6}$$

Add -3 and 8 to get 5.

$$\frac{1}{6}x+\frac{5}{6}$$

Expand

$$\frac{x+5}{6}$$

Solution Steps

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

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

Multiply \frac{1}{2} and 5 to get \frac{5}{2}.

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

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

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

Use the distributive property to multiply -\frac{1}{3} by 7x-4.

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

Express -\frac{1}{3}\times 7 as a single fraction.

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

Fraction \frac{-7}{3} can be rewritten as -\frac{7}{3} by extracting the negative sign.

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

Express -\frac{1}{3}\left(-4\right) as a single fraction.

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

Multiply -1 and -4 to get 4.

$$\frac{5}{2}x-\frac{1}{2}-\frac{7}{3}x+\frac{4}{3}$$

Combine \frac{5}{2}x and -\frac{7}{3}x to get \frac{1}{6}x.

$$\frac{1}{6}x-\frac{1}{2}+\frac{4}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{1}{6}x-\frac{3}{6}+\frac{8}{6}$$

Since -\frac{3}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}x+\frac{-3+8}{6}$$

Add -3 and 8 to get 5.

$$\frac{1}{6}x+\frac{5}{6}$$