Solve 02x+4/5y-(-2/5x)+1/10y+7/5y-2y

$$02 x + \frac { 4 } { 5 } y - ( - \frac { 2 } { 5 } x ) + \frac { 1 } { 10 } y + \frac { 7 } { 5 } y - 2 y$$

Evaluate

$$\frac{2x}{5}+\frac{3y}{10}$$

Solution Steps

Multiply 0 and 2 to get 0.

$$0x+\frac{4}{5}y-\left(-\frac{2}{5}x\right)+\frac{1}{10}y+\frac{7}{5}y-2y$$

Anything times zero gives zero.

$$0+\frac{4}{5}y-\left(-\frac{2}{5}x\right)+\frac{1}{10}y+\frac{7}{5}y-2y$$

Anything plus zero gives itself.

$$\frac{4}{5}y-\left(-\frac{2}{5}x\right)+\frac{1}{10}y+\frac{7}{5}y-2y$$

The opposite of -\frac{2}{5}x is \frac{2}{5}x.

$$\frac{4}{5}y+\frac{2}{5}x+\frac{1}{10}y+\frac{7}{5}y-2y$$

Combine \frac{4}{5}y and \frac{1}{10}y to get \frac{9}{10}y.

$$\frac{9}{10}y+\frac{2}{5}x+\frac{7}{5}y-2y$$

Combine \frac{9}{10}y and \frac{7}{5}y to get \frac{23}{10}y.

$$\frac{23}{10}y+\frac{2}{5}x-2y$$

Combine \frac{23}{10}y and -2y to get \frac{3}{10}y.

$$\frac{3}{10}y+\frac{2}{5}x$$

Factor

$$\frac{4x+3y}{10}$$

Solution Steps

Factor out \frac{1}{10}.

$$\frac{0+8y+4x+y+14y-20y}{10}$$

Consider 8y+4x+y+14y-20y. Multiply and combine like terms.

$$4x+3y$$

Rewrite the complete factored expression.

$$\frac{4x+3y}{10}$$