Solve (x-y+3)-2/3(6x-y-2)

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

Evaluate

$$-\frac{y}{3}-3x+\frac{13}{3}$$

Solution Steps

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

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

Express -\frac{2}{3}\times 6 as a single fraction.

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

Multiply -2 and 6 to get -12.

$$x-y+3+\frac{-12}{3}x-\frac{2}{3}\left(-1\right)y-\frac{2}{3}\left(-2\right)$$

Divide -12 by 3 to get -4.

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

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

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

Express -\frac{2}{3}\left(-2\right) as a single fraction.

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

Multiply -2 and -2 to get 4.

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

Combine x and -4x to get -3x.

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

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

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

Convert 3 to fraction \frac{9}{3}.

$$-3x-\frac{1}{3}y+\frac{9}{3}+\frac{4}{3}$$

Since \frac{9}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$-3x-\frac{1}{3}y+\frac{9+4}{3}$$

Add 9 and 4 to get 13.

$$-3x-\frac{1}{3}y+\frac{13}{3}$$

Expand

$$-\frac{y}{3}-3x+\frac{13}{3}$$

Solution Steps

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

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

Express -\frac{2}{3}\times 6 as a single fraction.

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

Multiply -2 and 6 to get -12.

$$x-y+3+\frac{-12}{3}x-\frac{2}{3}\left(-1\right)y-\frac{2}{3}\left(-2\right)$$

Divide -12 by 3 to get -4.

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

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

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

Express -\frac{2}{3}\left(-2\right) as a single fraction.

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

Multiply -2 and -2 to get 4.

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

Combine x and -4x to get -3x.

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

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

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

Convert 3 to fraction \frac{9}{3}.

$$-3x-\frac{1}{3}y+\frac{9}{3}+\frac{4}{3}$$

Since \frac{9}{3} and \frac{4}{3} have the same denominator, add them by adding their numerators.

$$-3x-\frac{1}{3}y+\frac{9+4}{3}$$

Add 9 and 4 to get 13.

$$-3x-\frac{1}{3}y+\frac{13}{3}$$