Solve 3/2x+y-6(2/3x+5/2y)=

$$\frac { 3 } { 2 } x + y - 6 ( \frac { 2 } { 3 } x + \frac { 5 } { 2 } y ) =$$

Evaluate

$$-\frac{5x}{2}-14y$$

Solution Steps

Use the distributive property to multiply -6 by \frac{2}{3}x+\frac{5}{2}y.

$$\frac{3}{2}x+y-6\times \frac{2}{3}x-6\times \frac{5}{2}y$$

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

$$\frac{3}{2}x+y+\frac{-6\times 2}{3}x-6\times \frac{5}{2}y$$

Multiply -6 and 2 to get -12.

$$\frac{3}{2}x+y+\frac{-12}{3}x-6\times \frac{5}{2}y$$

Divide -12 by 3 to get -4.

$$\frac{3}{2}x+y-4x-6\times \frac{5}{2}y$$

Express -6\times \frac{5}{2} as a single fraction.

$$\frac{3}{2}x+y-4x+\frac{-6\times 5}{2}y$$

Multiply -6 and 5 to get -30.

$$\frac{3}{2}x+y-4x+\frac{-30}{2}y$$

Divide -30 by 2 to get -15.

$$\frac{3}{2}x+y-4x-15y$$

Combine \frac{3}{2}x and -4x to get -\frac{5}{2}x.

$$-\frac{5}{2}x+y-15y$$

Combine y and -15y to get -14y.

$$-\frac{5}{2}x-14y$$

Expand

$$-\frac{5x}{2}-14y$$

Solution Steps

Use the distributive property to multiply -6 by \frac{2}{3}x+\frac{5}{2}y.

$$\frac{3}{2}x+y-6\times \frac{2}{3}x-6\times \frac{5}{2}y$$

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

$$\frac{3}{2}x+y+\frac{-6\times 2}{3}x-6\times \frac{5}{2}y$$

Multiply -6 and 2 to get -12.

$$\frac{3}{2}x+y+\frac{-12}{3}x-6\times \frac{5}{2}y$$

Divide -12 by 3 to get -4.

$$\frac{3}{2}x+y-4x-6\times \frac{5}{2}y$$

Express -6\times \frac{5}{2} as a single fraction.

$$\frac{3}{2}x+y-4x+\frac{-6\times 5}{2}y$$

Multiply -6 and 5 to get -30.

$$\frac{3}{2}x+y-4x+\frac{-30}{2}y$$

Divide -30 by 2 to get -15.

$$\frac{3}{2}x+y-4x-15y$$

Combine \frac{3}{2}x and -4x to get -\frac{5}{2}x.

$$-\frac{5}{2}x+y-15y$$

Combine y and -15y to get -14y.

$$-\frac{5}{2}x-14y$$