Solve 6(2/3x-y/4)-2(2x-y)

$$6 ( \frac { 2 } { 3 } x - \frac { y } { 4 } ) - 2 ( 2 x - y )$$

Evaluate

$$\frac{y}{2}$$

Short Solution Steps

Use the distributive property to multiply 6 by \frac{2}{3}x-\frac{y}{4}.

$$6\times \frac{2}{3}x+6\left(-\frac{y}{4}\right)-2\left(2x-y\right)$$

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

$$\frac{6\times 2}{3}x+6\left(-\frac{y}{4}\right)-2\left(2x-y\right)$$

Multiply 6 and 2 to get 12.

$$\frac{12}{3}x+6\left(-\frac{y}{4}\right)-2\left(2x-y\right)$$

Divide 12 by 3 to get 4.

$$4x+6\left(-\frac{y}{4}\right)-2\left(2x-y\right)$$

Express 6\left(-\frac{y}{4}\right) as a single fraction.

$$4x+\frac{-6y}{4}-2\left(2x-y\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x times \frac{4}{4}.

$$\frac{4\times 4x}{4}+\frac{-6y}{4}-2\left(2x-y\right)$$

Since \frac{4\times 4x}{4} and \frac{-6y}{4} have the same denominator, add them by adding their numerators.

$$\frac{4\times 4x-6y}{4}-2\left(2x-y\right)$$

Do the multiplications in 4\times 4x-6y.

$$\frac{16x-6y}{4}-2\left(2x-y\right)$$

Use the distributive property to multiply -2 by 2x-y.

$$\frac{16x-6y}{4}-4x+2y$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4x+2y times \frac{4}{4}.

$$\frac{16x-6y}{4}+\frac{4\left(-4x+2y\right)}{4}$$

Since \frac{16x-6y}{4} and \frac{4\left(-4x+2y\right)}{4} have the same denominator, add them by adding their numerators.

$$\frac{16x-6y+4\left(-4x+2y\right)}{4}$$

Do the multiplications in 16x-6y+4\left(-4x+2y\right).

$$\frac{16x-6y-16x+8y}{4}$$

Combine like terms in 16x-6y-16x+8y.

$$\frac{2y}{4}$$

Divide 2y by 4 to get \frac{1}{2}y.

$$\frac{1}{2}y$$

Expand

$$\frac{y}{2}$$

Short Solution Steps

Use the distributive property to multiply 6 by \frac{2}{3}x-\frac{y}{4}.

$$6\times \frac{2}{3}x+6\left(-\frac{y}{4}\right)-2\left(2x-y\right)$$

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

$$\frac{6\times 2}{3}x+6\left(-\frac{y}{4}\right)-2\left(2x-y\right)$$

Multiply 6 and 2 to get 12.

$$\frac{12}{3}x+6\left(-\frac{y}{4}\right)-2\left(2x-y\right)$$

Divide 12 by 3 to get 4.

$$4x+6\left(-\frac{y}{4}\right)-2\left(2x-y\right)$$

Express 6\left(-\frac{y}{4}\right) as a single fraction.

$$4x+\frac{-6y}{4}-2\left(2x-y\right)$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 4x times \frac{4}{4}.

$$\frac{4\times 4x}{4}+\frac{-6y}{4}-2\left(2x-y\right)$$

Since \frac{4\times 4x}{4} and \frac{-6y}{4} have the same denominator, add them by adding their numerators.

$$\frac{4\times 4x-6y}{4}-2\left(2x-y\right)$$

Do the multiplications in 4\times 4x-6y.

$$\frac{16x-6y}{4}-2\left(2x-y\right)$$

Use the distributive property to multiply -2 by 2x-y.

$$\frac{16x-6y}{4}-4x+2y$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -4x+2y times \frac{4}{4}.

$$\frac{16x-6y}{4}+\frac{4\left(-4x+2y\right)}{4}$$

Since \frac{16x-6y}{4} and \frac{4\left(-4x+2y\right)}{4} have the same denominator, add them by adding their numerators.

$$\frac{16x-6y+4\left(-4x+2y\right)}{4}$$

Do the multiplications in 16x-6y+4\left(-4x+2y\right).

$$\frac{16x-6y-16x+8y}{4}$$

Combine like terms in 16x-6y-16x+8y.

$$\frac{2y}{4}$$

Divide 2y by 4 to get \frac{1}{2}y.

$$\frac{1}{2}y$$