Solve 2/3(x+1)-1/2(x-5)

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

Evaluate

$$\frac{x+19}{6}$$

Solution Steps

Use the distributive property to multiply \frac{2}{3} by x+1.

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

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

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

Express -\frac{1}{2}\left(-5\right) as a single fraction.

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

Multiply -1 and -5 to get 5.

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

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

$$\frac{1}{6}x+\frac{2}{3}+\frac{5}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{1}{6}x+\frac{4}{6}+\frac{15}{6}$$

Since \frac{4}{6} and \frac{15}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}x+\frac{4+15}{6}$$

Add 4 and 15 to get 19.

$$\frac{1}{6}x+\frac{19}{6}$$

Expand

$$\frac{x+19}{6}$$

Solution Steps

Use the distributive property to multiply \frac{2}{3} by x+1.

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

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

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

Express -\frac{1}{2}\left(-5\right) as a single fraction.

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

Multiply -1 and -5 to get 5.

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

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

$$\frac{1}{6}x+\frac{2}{3}+\frac{5}{2}$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{5}{2} to fractions with denominator 6.

$$\frac{1}{6}x+\frac{4}{6}+\frac{15}{6}$$

Since \frac{4}{6} and \frac{15}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{6}x+\frac{4+15}{6}$$

Add 4 and 15 to get 19.

$$\frac{1}{6}x+\frac{19}{6}$$