Solve 1/2x+x-4/3x-1/2y+y-1/2y-3-2+1

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

Evaluate

$$\frac{x}{6}-4$$

Solution Steps

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

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

Combine \frac{3}{2}x and -\frac{4}{3}x to get \frac{1}{6}x.

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

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

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

Combine \frac{1}{2}y and -\frac{1}{2}y to get 0.

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

Subtract 2 from -3 to get -5.

$$\frac{1}{6}x-5+1$$

Add -5 and 1 to get -4.

$$\frac{1}{6}x-4$$

Factor

$$\frac{x-24}{6}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{x-24}{6}$$

Consider 3x+6x-8x-3y+6y-3y-18-12+6. Multiply and combine like terms.

$$x-24$$

Rewrite the complete factored expression.

$$\frac{x-24}{6}$$