Solve 5/6x-3/4y+z+3/4x-2y+1/2z

$$\frac { 5 } { 6 } x - \frac { 3 } { 4 } y + z + \frac { 3 } { 4 } x - 2 y + \frac { 1 } { 2 } z$$

Evaluate

$$\frac{3z}{2}+\frac{19x}{12}-\frac{11y}{4}$$

Solution Steps

Combine \frac{5}{6}x and \frac{3}{4}x to get \frac{19}{12}x.

$$\frac{19}{12}x-\frac{3}{4}y+z-2y+\frac{1}{2}z$$

Combine -\frac{3}{4}y and -2y to get -\frac{11}{4}y.

$$\frac{19}{12}x-\frac{11}{4}y+z+\frac{1}{2}z$$

Combine z and \frac{1}{2}z to get \frac{3}{2}z.

$$\frac{19}{12}x-\frac{11}{4}y+\frac{3}{2}z$$

Factor

$$\frac{19x-33y+18z}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{10x-9y+12z+9x-24y+6z}{12}$$

Consider 10x-9y+12z+9x-24y+6z. Multiply and combine like terms.

$$19x-33y+18z$$

Rewrite the complete factored expression.

$$\frac{19x-33y+18z}{12}$$