Solve 6/8x-3/4y-5/6x-7+2/3y

$$\frac { 6 } { 8 } x - \frac { 3 } { 4 } y - \frac { 5 } { 6 } x - 7 + \frac { 2 } { 3 } y$$

Evaluate

$$-\frac{x}{12}-\frac{y}{12}-7$$

Solution Steps

Reduce the fraction \frac{6}{8} to lowest terms by extracting and canceling out 2.

$$\frac{3}{4}x-\frac{3}{4}y-\frac{5}{6}x-7+\frac{2}{3}y$$

Combine \frac{3}{4}x and -\frac{5}{6}x to get -\frac{1}{12}x.

$$-\frac{1}{12}x-\frac{3}{4}y-7+\frac{2}{3}y$$

Combine -\frac{3}{4}y and \frac{2}{3}y to get -\frac{1}{12}y.

$$-\frac{1}{12}x-\frac{1}{12}y-7$$

Factor

$$\frac{-x-y-84}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{9x-9y-10x-84+8y}{12}$$

Consider 9x-9y-10x-84+8y. Multiply and combine like terms.

$$-x-y-84$$

Rewrite the complete factored expression.

$$\frac{-x-y-84}{12}$$