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

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

Evaluate

$$\frac{-3x-9}{2}$$

Solution Steps

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

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

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

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

Multiply -3 and 3 to get -9.

$$\frac{-9}{2}-\frac{3}{2}y+\frac{3}{2}\left(y-x\right)$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$-\frac{9}{2}-\frac{3}{2}y+\frac{3}{2}\left(y-x\right)$$

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

$$-\frac{9}{2}-\frac{3}{2}y+\frac{3}{2}y+\frac{3}{2}\left(-1\right)x$$

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

$$-\frac{9}{2}-\frac{3}{2}y+\frac{3}{2}y-\frac{3}{2}x$$

Combine -\frac{3}{2}y and \frac{3}{2}y to get 0.

$$-\frac{9}{2}-\frac{3}{2}x$$

Expand

$$\frac{-3x-9}{2}$$

Solution Steps

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

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

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

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

Multiply -3 and 3 to get -9.

$$\frac{-9}{2}-\frac{3}{2}y+\frac{3}{2}\left(y-x\right)$$

Fraction \frac{-9}{2} can be rewritten as -\frac{9}{2} by extracting the negative sign.

$$-\frac{9}{2}-\frac{3}{2}y+\frac{3}{2}\left(y-x\right)$$

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

$$-\frac{9}{2}-\frac{3}{2}y+\frac{3}{2}y+\frac{3}{2}\left(-1\right)x$$

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

$$-\frac{9}{2}-\frac{3}{2}y+\frac{3}{2}y-\frac{3}{2}x$$

Combine -\frac{3}{2}y and \frac{3}{2}y to get 0.

$$-\frac{9}{2}-\frac{3}{2}x$$