Solve 1/3(x+3y-4z)+1/2(6-2y-3z)

$$\frac { 1 } { 3 } ( x + 3 y - 4 z ) + \frac { 1 } { 2 } ( 6 - 2 y - 3 z )$$

Evaluate

$$\frac{x}{3}-\frac{17z}{6}+3$$

Solution Steps

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

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

Cancel out 3 and 3.

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

Multiply \frac{1}{3} and -4 to get \frac{-4}{3}.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

Use the distributive property to multiply \frac{1}{2} by 6-2y-3z.

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

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

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

Divide 6 by 2 to get 3.

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

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

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

Divide -2 by 2 to get -1.

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

Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.

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

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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

Combine y and -y to get 0.

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

Combine -\frac{4}{3}z and -\frac{3}{2}z to get -\frac{17}{6}z.

$$\frac{1}{3}x-\frac{17}{6}z+3$$

Expand

$$\frac{x}{3}-\frac{17z}{6}+3$$

Solution Steps

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

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

Cancel out 3 and 3.

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

Multiply \frac{1}{3} and -4 to get \frac{-4}{3}.

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

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

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

Use the distributive property to multiply \frac{1}{2} by 6-2y-3z.

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

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

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

Divide 6 by 2 to get 3.

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

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

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

Divide -2 by 2 to get -1.

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

Multiply \frac{1}{2} and -3 to get \frac{-3}{2}.

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

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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

Combine y and -y to get 0.

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

Combine -\frac{4}{3}z and -\frac{3}{2}z to get -\frac{17}{6}z.

$$\frac{1}{3}x-\frac{17}{6}z+3$$