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

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

Evaluate

$$-\frac{4z}{3}-\frac{7y}{6}-\frac{13x}{12}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{y}{2} times \frac{2}{2}.

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

Since \frac{x}{4} and \frac{2y}{4} have the same denominator, add them by adding their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply z times \frac{4}{4}.

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

Since \frac{x+2y}{4} and \frac{4z}{4} have the same denominator, add them by adding their numerators.

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

Multiply -\frac{1}{3} times \frac{x+2y+4z}{4} by multiplying numerator times numerator and denominator times denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -x-y-z times \frac{3\times 4}{3\times 4}.

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

Since \frac{-\left(x+2y+4z\right)}{3\times 4} and \frac{\left(-x-y-z\right)\times 3\times 4}{3\times 4} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -\left(x+2y+4z\right)+\left(-x-y-z\right)\times 3\times 4.

$$\frac{-x-2y-4z-12x-12y-12z}{3\times 4}$$

Combine like terms in -x-2y-4z-12x-12y-12z.

$$\frac{-13x-14y-16z}{3\times 4}$$

Expand 3\times 4.

$$\frac{-13x-14y-16z}{12}$$

Expand

$$-\frac{4z}{3}-\frac{7y}{6}-\frac{13x}{12}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{y}{2} times \frac{2}{2}.

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

Since \frac{x}{4} and \frac{2y}{4} have the same denominator, add them by adding their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply z times \frac{4}{4}.

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

Since \frac{x+2y}{4} and \frac{4z}{4} have the same denominator, add them by adding their numerators.

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

Multiply -\frac{1}{3} times \frac{x+2y+4z}{4} by multiplying numerator times numerator and denominator times denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply -x-y-z times \frac{3\times 4}{3\times 4}.

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

Since \frac{-\left(x+2y+4z\right)}{3\times 4} and \frac{\left(-x-y-z\right)\times 3\times 4}{3\times 4} have the same denominator, add them by adding their numerators.

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

Do the multiplications in -\left(x+2y+4z\right)+\left(-x-y-z\right)\times 3\times 4.

$$\frac{-x-2y-4z-12x-12y-12z}{3\times 4}$$

Combine like terms in -x-2y-4z-12x-12y-12z.

$$\frac{-13x-14y-16z}{3\times 4}$$

Expand 3\times 4.

$$\frac{-13x-14y-16z}{12}$$