Solve 1/3(-1+x)+1/2(x+y)-7/6

$$\frac { 1 } { 3 } ( - 1 + x ) + \frac { 1 } { 2 } ( x + y ) - \frac { 7 } { 6 }$$

Evaluate

$$\frac{y}{2}+\frac{5x}{6}-\frac{3}{2}$$

Solution Steps

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

$$\frac{1}{3}\left(-1\right)+\frac{1}{3}x+\frac{1}{2}\left(x+y\right)-\frac{7}{6}$$

Multiply \frac{1}{3} and -1 to get -\frac{1}{3}.

$$-\frac{1}{3}+\frac{1}{3}x+\frac{1}{2}\left(x+y\right)-\frac{7}{6}$$

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

$$-\frac{1}{3}+\frac{1}{3}x+\frac{1}{2}x+\frac{1}{2}y-\frac{7}{6}$$

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

$$-\frac{1}{3}+\frac{5}{6}x+\frac{1}{2}y-\frac{7}{6}$$

Least common multiple of 3 and 6 is 6. Convert -\frac{1}{3} and \frac{7}{6} to fractions with denominator 6.

$$-\frac{2}{6}+\frac{5}{6}x+\frac{1}{2}y-\frac{7}{6}$$

Since -\frac{2}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2-7}{6}+\frac{5}{6}x+\frac{1}{2}y$$

Subtract 7 from -2 to get -9.

$$\frac{-9}{6}+\frac{5}{6}x+\frac{1}{2}y$$

Reduce the fraction \frac{-9}{6} to lowest terms by extracting and canceling out 3.

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

Expand

$$\frac{y}{2}+\frac{5x}{6}-\frac{3}{2}$$

Solution Steps

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

$$\frac{1}{3}\left(-1\right)+\frac{1}{3}x+\frac{1}{2}\left(x+y\right)-\frac{7}{6}$$

Multiply \frac{1}{3} and -1 to get -\frac{1}{3}.

$$-\frac{1}{3}+\frac{1}{3}x+\frac{1}{2}\left(x+y\right)-\frac{7}{6}$$

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

$$-\frac{1}{3}+\frac{1}{3}x+\frac{1}{2}x+\frac{1}{2}y-\frac{7}{6}$$

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

$$-\frac{1}{3}+\frac{5}{6}x+\frac{1}{2}y-\frac{7}{6}$$

Least common multiple of 3 and 6 is 6. Convert -\frac{1}{3} and \frac{7}{6} to fractions with denominator 6.

$$-\frac{2}{6}+\frac{5}{6}x+\frac{1}{2}y-\frac{7}{6}$$

Since -\frac{2}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-2-7}{6}+\frac{5}{6}x+\frac{1}{2}y$$

Subtract 7 from -2 to get -9.

$$\frac{-9}{6}+\frac{5}{6}x+\frac{1}{2}y$$

Reduce the fraction \frac{-9}{6} to lowest terms by extracting and canceling out 3.

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