Solve -5(2/5x-1/10y+2)+4(1/2x-1/8y+1)

$$- 5 ( \frac { 2 } { 5 } x - \frac { 1 } { 10 } y + 2 ) + 4 ( \frac { 1 } { 2 } x - \frac { 1 } { 8 } y + 1 )$$

Evaluate

$$-6$$

Solution Steps

Use the distributive property to multiply -5 by \frac{2}{5}x-\frac{1}{10}y+2.

$$-5\times \frac{2}{5}x-5\left(-\frac{1}{10}\right)y-10+4\left(\frac{1}{2}x-\frac{1}{8}y+1\right)$$

Multiply -5 times \frac{2}{5}.

$$-2x-5\left(-\frac{1}{10}\right)y-10+4\left(\frac{1}{2}x-\frac{1}{8}y+1\right)$$

Express -5\left(-\frac{1}{10}\right) as a single fraction.

$$-2x+\frac{-5\left(-1\right)}{10}y-10+4\left(\frac{1}{2}x-\frac{1}{8}y+1\right)$$

Multiply -5 and -1 to get 5.

$$-2x+\frac{5}{10}y-10+4\left(\frac{1}{2}x-\frac{1}{8}y+1\right)$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$-2x+\frac{1}{2}y-10+4\left(\frac{1}{2}x-\frac{1}{8}y+1\right)$$

Use the distributive property to multiply 4 by \frac{1}{2}x-\frac{1}{8}y+1.

$$-2x+\frac{1}{2}y-10+4\times \frac{1}{2}x+4\left(-\frac{1}{8}\right)y+4$$

Multiply 4 and \frac{1}{2} to get \frac{4}{2}.

$$-2x+\frac{1}{2}y-10+\frac{4}{2}x+4\left(-\frac{1}{8}\right)y+4$$

Divide 4 by 2 to get 2.

$$-2x+\frac{1}{2}y-10+2x+4\left(-\frac{1}{8}\right)y+4$$

Express 4\left(-\frac{1}{8}\right) as a single fraction.

$$-2x+\frac{1}{2}y-10+2x+\frac{4\left(-1\right)}{8}y+4$$

Multiply 4 and -1 to get -4.

$$-2x+\frac{1}{2}y-10+2x+\frac{-4}{8}y+4$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

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

Combine -2x and 2x to get 0.

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

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

$$-10+4$$

Add -10 and 4 to get -6.

$$-6$$

Factor

$$-6$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{-\left(4x-y+20\right)+4x-y+8}{2}$$

Simplify.

$$-6$$